Hello. As a tile installer, I have removed many baseboards over the years. In your case, the goal is to remove it without damaging the wall or baseboard.

The first thing I would do is use a sharp razor knife to carefully cut the caulked top edge of the baseboard, cutting in a gentle, downward angle. This is extremely important, because if you do not cut the caulked edge, you may end up ripping off a thin layer of your drywall above the baseboard!

Next, I would try to remove the baseboard with the quarter round still attached. I like to use a metal putty knife (and hammer if necessary) to pry one end of the baseboard away from the wall. Do this by placing the putty knife on the top edge of the baseboard against the wall. Tap and pry downward until you get a little separation.

Next using a flat pry bar work your way down the wall and pry against the wall section that is BEHIND your baseboard. With a little patience and carefulness, you should end up an intact baseboard. Good luck!