How can I modify this dryer vent cap to keep lint from getting trapped?
I cannot say I'm a fan of the design of that vent - although looking at your other question, I'm rather surprised that lint is falling down into that gap.  Possibly your fan is creating too much pressure, and it's backing up inside the vent at the 180 and thus air is escaping through the pushing some lint down into that gap, where it can get stuck.

If that's the case, then you might try installing a baffle inside the vent to force lint up far enough in the vent so that it has to go out the intended port, but which still allows water out.  Like so...


Sorry, the color doesn't show well, but inside I've added a piece of metal running from just below the intake port to nearly the end of the angled portion of the vent, with a brace connecting it to the body to keep it stable.  You can't see it but there should be drip holes at the point where the new plate hits the flashing for water drainage.

The idea being, lint flies in and cannot be forced directly down to the gap in question, but water will hit the tray, run back and go through the drip holes.

That or replace it with this