Have you played vs a Link yet or am I just doing something wrong? Once he brings out the boomerang, I'm forced to approach.
I "main" Link and as you know relatively recently Link's boomerang was changed to have less start and end lag for combo-ing and keeping space (unless I'm wrong) but the drawback is that it has less reach (still good distance). Typically a Link will 1. Get a bomb 2. Charge an arrow (can jump and fire an uncharged one so it hits from above) 3. Approach 4. Stand still?
Canceling the boomerang with an arrow will just allow Link to throw another in a couple of seconds. Fortunately Pit can curve his arrows. This allows him to punish a bomb pull (he'll still get the bomb), stop Link from CHARGING an arrow (Jump uncharged arrow will still fire I think). An approaching Link that follows his boomerang can just power shield your arrow so I would do a retreating arrow through the use of a turn around B (hitting back BEFORE hitting b and releasing it to neutral). Pit's arrows are infinite so you can stay out of range of his boomerang and pressure him for throwing it (if you're too far away you have to read him as he'll have time to defend).
Of course Pit can eat up distance fairly quickly with WoI so you might be able to Powershield the boomerang (destroying it) and WoI towards him. If he's pulling a bomb then you get a free punish/string. Of course make sure he doesn't read you or you'll eat an F-Smash, Nair, or Fair (probably). To prevent this you may be able to quick drop to the ground (slamming down and hitting B at the same time?) and then punish (if it was an F-Smash make sure you look out for the second hit though).
Links will throw your boomerang diagonal so it ends up above you, this is to limit your options (you might be able to just WoI to him but if you do try to cross him up so the boomerang won't get you from behind).
If nair eats boomerang then that helps a lot, WoI and nair through it if you're close enough.
I'd just stay really mobile and close enough to punish if the opportunity arises, don't forget you can WoI back and forth for some quick movement. Play like CF or Fox and abuse your options out of WoI so Link can't corner you.
Remember this is all theory so if anyone can test this that would be nice, LOL.