No, in contemporary native English it is called "an exchange of pleasantries." A Google Ngram confirms my native knowledge that this is much more common in our time then "exchange of civilities."
Note the Oxford Dictionary:
Pleasantry:
(usually pleasantries)
An inconsequential remark made as part of a polite conversation:
'after an exchange of pleasantries, I proceeded to outline a plan'
More example sentences
And off we both went through the rain, pleasantries exchanged and honour satisfied.
After the introductions were done they exchanged pleasantries with Caitlyn who answered politely to all of them.
Johnson attempted to start conversation with some pleasantries but Bill was not very talkative.
The same dictionary gives one example sentence with exchanging civilities, but Google Ngrams confirms that pleasantries is much more common these days.
