Did my sling purposely drag a cricket out of it's "nest and add it as an ornament to it web. If I want to get it out I'll hafta do some damage to the web that it's building and I don't really want to do that. Any suggestions?
Yeah, I don't think that T's or spiders in general get "pissed off" when their webs are disturbed or anything like that... it happens in the wild all the time, they just re-create them. As soon as you're gone, instinct will kick in and they will begin repairing the web, probably without even thinking about it.
You won't be causing your T any stress if you pull the junk out of his web... which, btw, you will want to do anyway to avoid bigger problems like fungus or mold.