The easiest solution is to avoid the problem to begin with. If you keep the hook and loop fastened together when washing, the hook should not get hung up with lint and other detritus. This is also something to consider when deciding which side of the fasteners goes on which item. For instance, if you plan to wash one item frequently, it may make sense to apply the loop side to that item instead of the hook side.
Hook material is often inexpensive enough that if you have a single piece that is dirty or rendered unusable because it has collected so much debris, it may be easier to cut or remove that piece of hook and replace it with a new piece. Even a 25 yard roll of sew on material can cost as little as $9.75.
Now we're getting into ways to actually clean out a portion of hook. Using a comb or brush can make a significant impact on all of that junk that has collected over time. The individual hooks on the hook side are evenly spaced, so you should be able to find the rows of hooks and the rows between them where you can pass your comb or brush through to start cleaning. Cleaning VELCRO® Brand products is time consuming and you may not get it spotless, but you should be able to make a sizable impact on its performance once you've finished.