You have your answer about which person in the Tea Bag Party is responsible for the unfortunate name. Grinch offered it to you. I'm sure the guy never would have made the suggestion about tea bags if he'd been in that particular loop, but there you go. People make unfortunate connections for innocent reasons all the time. You needn't get defensive about these things, in this case it's not even remotely your fault, and the linguistic connection remains. It's still funny/odd, and we all need to live with it.
In England, when somebody wants to say that they'll stop by to say hello, the idiom is, "I'll knock you up." Innocent English folk will often look completely puzzled when Americans burst into laughter. Are you going to say that the English need to change their long-standing idiom or that Americans need to change their dirty little minds?
You could try.
In the reverse, in American English, it's customary to talk about somebody on occasion "falling on their fanny." The English would say "arse." Were you to say "fanny," there is a percentage of the more uptight English folk who would take offense at an exceedingly indelicate usage descriptive of a close by anatomical female feature. No problem for us colonials, not generally good for tea with the vicar, however, depending of course on the vicar.
Tea bags are the sub-cultural equivalent.
Your subcultural literacy may be far broader than I would otherwise credit, but somehow I would expect it not to be the case; nor would I expect this to be the case with many Tea Party members. It's actually I think impoliteness on the left that puts you in this position, as if you would have reason to know this stuff, and that not knowing makes you foolish. It's simple bad manners to poke fun at the lack of knowledge.
The content of the lack of knowledge itself, however, while not your fault at all, is very much ironic, and is for that reason if for no other, very funny indeed.
I don't know if you are at all fond of The Stephen Hunter novels. Hunter is a very fine novelist and has written a series of novels about the adventure of a Vietnam era Sniper and his attempts to settle into the modern world. Mr. Hunter is not fond of the American left, and his most recent book, I, Sniper — which I loved — plays a similar sort of trick on the ignorance of the American left about firearms.
If you're a Jane Fonda hater — as I am not; I admire her brio, talent and integrity — you'll be happy to see what is done to the character that represents her and the various other left leaning characters in the Novel. I found the various events tolerable in that sense only by Mr. Hunter's extraordinary skills as a novelist. He won a Pulitzer for his books of Movie reviews, but I believe his fiction is at least as skilled though not politically congenial for me personally. Doesn't stop me from reading the stuff. though.