If a parody is used in a non-critical means, as in, the idea is being parodied, does it infringe copyright?

A club at my school found a t-shirt design online and they wanted to use it as the club shirt. I was a little hesitant and they said not to worry they would change it up a little. (The design is a word search type thing and they said they would mix up the letters.) I am still hesitant that that might be an infringement on copyright, but am not sure. Can anyone tell me what copyright law says about this?