Can't remove screen from bottom of dishwasher
Those are called "push nuts" and they can be quite difficult to remove.  I've been most successful by inserting a thin screwdriver underneath the nut and gently prying up as you work your way around.

Alternatively, you can try to snap the nut by prying up an edge and then using a pair of needle-nose pliers to twist the edge until it breaks.

Another approach is to take a pick and pry up the teeth that are biting into the post so that they release.  You'll need to bend them far enough so that after you remove the pick they don't bite back into the post.  Work your way around and release all the teeth.

In either case the nut is unlikely to be reusable so you'll need to find some replacements.  I've seen them at well-stocked hardware stores or home centers and you can find many online suppliers after searching for "push nuts".

Try to avoid breaking the post itself as it appears to be plastic.

Are you sure you need to removed that screen?  It doesn't appear that the manufacturer intended for it to be removable, at least not easily for cleaning.  It appears to me that nothing large enough to clog the drain should fit through that screen.