Christian Hupfer in How to label a restated theorem? and Cragfelt in How to get a restated tcolorbox to appear in the list of tcolorboxes both used label={dft:1-1a} for the restated tcolorbox but here it refers to Subsection 1.1.2 dft:1-1.
\documentclass[11pt]{book}
\usepackage{amsmath}
\usepackage{makeidx}
\makeindex
\usepackage{tcolorbox}%---This is where the PACKAGE must be.
\tcbuselibrary{%Begin load libraries for tcolorbox
skins,%
raster,%
breakable,%
xparse,%
}%End load libraries for tcolorbox
% \usepackage{xparse}%
%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$Begin HYPERREF
\usepackage[hyperfootnotes=false]{hyperref}%[pdfborder={0 0 0}]
%Begin the ``quick and dirty hack'' due to Heiko Oberdiek which loads showidx
\makeatletter
\ifHy@hyperindex
\def\HyInd@ParenLeft{(}%
% Hook in \HyInd@@wrindex
\let\HyInd@showidx\@empty
% Hook in \HyInd@@wrindex for package showidx
\def\HyInd@showidx#1{%
\@showidx{#1}%
\if@nobreak
\ifvmode
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}%
% Load package showidx
\let\siOrg@makeindex\makeindex
\let\siOrg@@index\@index
\let\siOrg@@wrindex\@wrindex
\let\siOrg@index\index
\RequirePackage{showidx}
\let\makeindex\siOrg@makeindex
\let\@index\siOrg@@index
\let\@wrindex\siOrg@@wrindex
\let\index\siOrg@index
% rest of hyperref part
\@ifpackageloaded{multind}{%
\let\HyInd@org@wrindex\@wrindex
\def\@wrindex#1#2{\HyInd@@wrindex{#1}#2||\\}%
\def\HyInd@@wrindex#1#2|#3|#4\\{%
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\HyInd@org@wrindex{#1}{#2|hyperpage}%
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HyInd@org@wrindex{#1}{#2|#3hyperpage}%
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\HyInd@org@wrindex{#1}{#2|#3}%
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\def\@wrindex#1{\@@wrindex#1||\\}
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\string\indexentry{#1|hyperpage}{\thepage}%
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\endgroup
\HyInd@showidx{#1}%
\@esphack
}%
}%
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%End the ``quick and dirty hack'' due to Heiko Oberdiek which loads showidx
\hypersetup{%begin colors
colorlinks,
linkcolor={red!50!black},
% citecolor={blue!50!black},
% urlcolor={blue!80!black}
}%end colors
%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ End HYPERREF
\usepackage{cleveref}
\Crefname{subsection}{Subsection}{Subsection}
\newcommand{\titleref}{\nameref}%displays title of reference as is.
%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Begin References
%sssssssssssssssssssssssssssssssssss Begin Sharpe Schulz (2016-02-1) for math in showid
\let\oldopenparen\(
\let\oldcloseparen\)
\def\({\protect\oldopenparen}
\def\){\protect\oldcloseparen}
%sssssssssssssssssssssssssssssssssss End Sharpe Schulz (2016-02-1) for math in showid
%sssssssssssssssssssssssssssssssssss Begin Hupfer code
%============== Begin prelim
\makeatletter
\def\first@up#1#2\relax{\uppercase{#1}#2}%
\newcommand{\FirstUpcase}[1]%
{\expandafter\expandafter\expandafter\first@up#1\relax}%
\makeatother
%---------------------
\makeatletter
\def\first@low#1#2\relax{\lowercase{#1}#2}%
\newcommand{\FirstLowcase}[1]%
{\expandafter\expandafter\expandafter\first@low#1\relax}%
\makeatother
%============== End prelim
%============== Begin TitleRef = lower to upper
\NewDocumentCommand%
{\TitleRef}{sm}%
{%begin definition
\IfBooleanTF{#1}%
{%
\FirstUpcase{\getrefbykeydefault{#2}{name}{-1}}%
}%
{%
\IfRefUndefinedExpandable{#2}{}%
{% begin label is defined, now get hyperlink
\hyperlink{\getrefbykeydefault{#2}{anchor}{-1}}%creates the link
{\FirstUpcase{\getrefbykeydefault{#2}{name}{-1}}}%error otherwise
}% end label is defined, now get hyperlink
}%
}%end definition
%============== End TitleRef = lower to upper
%============== Begin titleRef = upper to lower
\NewDocumentCommand%
{\titleRef}{sm}%
{%begin definition
\IfBooleanTF{#1}%
{%
\FirstLowcase{\getrefbykeydefault{#2}{name}{-1}}%
}%
{%
\IfRefUndefinedExpandable{#2}{}%
{% begin label is defined, now get hyperlink
\hyperlink{\getrefbykeydefault{#2}{anchor}{-1}}%
{\FirstLowcase{\getrefbykeydefault{#2}{name}{-1}}}%
}% end label is defined, now get hyperlink
}% end if false
}%definition
%============== End titleRef = upper to lower
%sssssssssssssssssssssssssssssssssss End Hupfer code
%sssssssssssssssssssssssssssssssssss Begin Andrew code for ref to indexed words
%============== Begin the Andrew code as edited Oct 27 at 17:24
\newcommand{\INDEX}[2][]{\phantomsection%
\if\relax\detokenize{#1}\relax\index{#2}\label{ind:#2}%
\else\index{#2}\label{ind:#1}\fi%
}%End INDEX
\newcommand{\DEX}[2][]{%
\if\relax\detokenize{#1}\relax\hyperref[ind:#2]{#2}%
% (\Cpageref{ind:#2})%
\else\hyperref[ind:#1]{#2}%
%(\Cpageref{ind:#1})%
\fi%
}%End DEX
%============== End the Andrew code as edited Oct 27 at 17:24
%============== Begin To make Cpageref work.
\newcommand{\PGX}[2][]{%
\if\relax\detokenize{#1}%
\relax%
% \hyperref[ind:#2]{#2}%
\Cpageref{ind:#2}%
\else%
% \hyperref[ind:#1]{#2}%
\Cpageref{ind:#1}%
\fi%
}%
%End To make Cpageref work.
%sssssssssssssssssssssssssssssssssss End Andrew code for ref to indexed words
%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ End References
%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Begin new tcolorbox - COMMANDS must be after cleveref.
\newcounter{dft}%
\newtcolorbox%
[%beginForReferences
use counter= dft,
number within=chapter,
list inside= dft,%creates the list under tcblistof
crefname={definition}{definitions},
Crefname={Definition}{Definitions},
]%endForReferences
{efinition}%
[2][]%
{%
detach title,
coltitle=black,
nameref={#2},%
before upper={\tcbtitle\quad},%
%code={\gdef\mytitleagree{\textbf{#2}}},%%Used to include mytitle in the ``number''
title=DEFINITION \thetcbcounter \, #2,%
nameref=#2,%
list entry={DEFINITION ~\thetcbcounter ~ #2},%
#1,%Required for references.
}%
%=======Begin To restate an already stated definition STURM after YASMAR
\newtcolorbox%
[%beginForReferences
list inside= dft,
]%endForReferences
{efinitionRphr}%
[3][]%
{%
detach title,%This prevents the top from being the color of the frame
before upper={\tcbtitle\quad},%This prevents the top from being the color of the frame
enhanced,%
arc=0.2mm,%
colback= yellow,%
colframe= black,%
coltitle=black,%
title= DEFINITION (Restated) ~\ref{#2}~\nameref{#2},%
nameref={#2},%
list entry= DEFINITION (Restated) ~\ref{#2}~\nameref{#2},
#1%
}%
%=======End To restate an already stated definition STURM after YASMAR
%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ End new tcolorbox
\begin{document}
\chapter{ONE}\label{1-0-0}
\newpage
\section{Height}\label{1-1-0}
\newpage
\subsection{extremes}\label{1-1-1}
A \textbf{minimum}\INDEX[]{minimum} is an input \textbf{$\boldsymbol{x_{\text{min}}}$}\INDEX[xmin]{$x_{\text{min}}$} whose output is smaller that the outputs of nearby inputs.
\begin{efinition}[label={dft:1-1}]{Maximum}
An input \textbf{$\boldsymbol{x_{\text{max}}}$} whose output is larger than the outputs of nearby inputs
\end{efinition}
\newpage
\subsection{far-fetched}\label{1-1-2}
\begin{efinitionRphr}[label={dft:1-1a}]{dft:1-1}{~}
The biggest of all
\end{efinitionRphr}
%
\chapter{References}\label{2-0-0}
\textbf{To avoid confusion, \emph{nameref} was RenewCommanded as \emph{titleref}.}
\emph{nameCref+labelcref+titleref}:\hspace{8mm} \nameCref{dft:1-1} \labelcref{dft:1-1} \titleref{dft:1-1}
\emph{nameCref+labelcref+titleref}:\hspace{8mm} \nameCref{dft:1-1a} \labelcref{dft:1-1a} \titleref{dft:1-1a}
\tcblistof[\chapter]{dft}{List of Definitions}
\phantomsection%otherwise, clicking on index in toc gets to GNU
\printindex
\end{document}
imakeidxpackage instead ofmakeidx? – Dec 21 '17 at 05:36dft:1-1awas introduced by the O.P. not by me, by the way – Dec 21 '17 at 05:43nameref={#2}in the repeated box will give the restated definition the name reference of the label -- I doubt that you want to have this effect? – Dec 21 '17 at 06:25