とんでもねぇもん掴ませてくれたな= とんでもないもの掴ませてくれたな
The character speaking got this file from his station and it's giving them to the other characters.
What's I'm stumbled is this use of "くれた".
From context my interpretation would be something akin to "What a terrible thing you made me get", however I'm not really sure. The くれた feels like he could be used sarcastically?
"you let me get" doesn't make much sense. He got the file for them.
It is an idiomatic meaning exclusive to the causative form つかませる. Although つかむ itself has a somewhat relevant connotation "to grab (some important information)", つかませる also has a distinct sense: "foist (goods) on someone (resulting giver's benefit or receiver's trouble)". This usually suggest the other one directly gives you something, but also applicable when they command, solicit, inspire, allow, etc. you to have (or in a sense, used to blame one's bad decision on the other).
偽のダイヤの指輪をつかませられた
I had a fake diamond ring palmed [passed] off on me.
(from プログレッシブ和英中辞典)
So, in this context, the speaker is complaining that the other one handed off caused him to have such a "hot potato". And くれる is used in a sarcastic way as you say, and as linked in the comment: Using くれる for doing something bad.
