What can you do if someone changes your words (or tune for that matter)? Well if they do it commercially you can sue. There are plenty lawyers who'd be willing to take you money.
Otherwise, I don't see that you have any choice in the matter. Do you go round and listen at doors to make sure people are singing the right words while they're doing the dishes?
And have you ever been past a children's playground and heard what THEY do to songs? When my kids where younger Billy Joel's "Uptown Girl" started "Uptown dolly, she been living in a Tesco trolley." I don't think he would appreciate that (well he might since the divorce).
The analogy with paintings and poetry is interesting but the argument is flawed. Once a work of art is "out there' the artist has no control over how it is interpreted. Many people completely "misunderstand" what a poet, painter or writer is trying to say. The difference we are talking about here is that a singer passes on his interpretation to someone else.
Personally I'm not too bothered if someone alters my songs, provided they say so and credit me as the original writer, though I might object if they change the whole meaning of it.
Worse things happen. There are some singers who could sing all the correct words and still ruin the song completely!