Marshall was an environmental lawyer, and while he had stints in corporate law, creative license laws wouldn't have been his area of expertise. (You can read his character's bio here.) And even if Ted had easy access to the right kind of lawyer, and it actually occurred to him that the movie was a suit-worthy offense (that wouldn't just end up being an expensive hassle), it would be incredibly difficult to prove that a movie like "The Wedding Bride," which claims to be entirely fictitious, is actually libel. Not impossible, but definitely difficult to the point that it likely wouldn't have been worth it to sue. This conversation on TV Tropes does a pretty good job of discussing this and other reasons why Ted wouldn't want to sue (though honestly it may not even have seriously occurred to him as a viable option).
Some good quotes from the conversation include:
While there was obvious "Ted Mosby" influence in the movie's villain...
I hate to do it, but I've got to cite Unreliable Narrator here. Ted
was listening for Ted Mosby, so he heard it. I really do doubt the
actors would say Ted Mosby without asking some questions, and no one
else heard it. It makes a lot more sense.
That isn't to say that the villain wasn't based on Ted Mosby - he definitely was - but Ted is likely blowing it out of proportion. So it's hard to say whether the resemblance was big enough that Ted could be reasonably sure he'd win a court case. At least, sure enough to shell out the money and go through all the public exposure that would come out of it:
...he'd be putting himself out there in public, claiming that the
A-Hole in the movie was based on him, and demanding royalties for a
movie he didn't make. Ted wouldn't want to endure that sort of
negative exposure. Who would?
Suing over the movie may just bring bigger attention to the issue and have more people - many of them complete strangers - associate him with the character and the movie than just his closest friends who already know Ted's history with Stella and her ex-ex-husband.