I’m having a hard time understanding this entire post and I think it’s because I don’t understand the opening paragraphs. It sounds to me like Alice’s node has a transaction and Bob’s node sent her an inv or a sketch with the wtxid, so Alice knows Bob has a validated copy of the transaction. Given that, a particular instance of the general question you seem to be asking is, “should Alice send Bob an inv for that transaction?”
That doesn’t make sense to me. Why would Alice ever tell Bob about a transaction she knows that he already has?
When you say “peers who already know about it”, do you mean something else? Like peers we think know about a transaction, based on probabilistic reasoning?
Sorry if I’m missing something obvious and thank your for your work on Erlay!