to try to get information from someone or from a situation without asking direct questions
试探出…的意见（或态度），摸清

Why don’t you feel them out to see if they’ll invite me over too? 你为什么不跟他们试探一下，看看他们是不是也会邀请我？

I think they are trying to feel out what the new relationship should be. 我想他们还在试探新的关系应该是什么样的。