Is there a word or short phrase for when someone brings up a topic then tries to drop it or move on from it?

I am curious as to if there is a phrase or word for when some one brings something up then tries to drop it.

I suffer mild OCD and my biggest trigger and cause of a lot of ruined social encounters are the events when somebody goes... "Last Thursday.... Oh sorry dont worry I never should have mentioned that" Or "I had this great story... But I shouldn't say" This seems to happen a lot around me, so I wondered if it has a name as it must happen around others too, even if they are able to accept it needn't be discussed. Thanks very much !

It's not specific to conversation, but:

Backpedal v. Reverse one's previous action or opinion.

seems like it would cover it, eg:

Anne started to talk about last night's barbecue, but backpedalled when she remembered that Bob was vegetarian.