Solid Hardwood, Engineered and Laminate Flooring - Best way to remove quarter round??

What is the best method or tools to use to remove quarter round to minimize damage?

You can drive the nail through with nail punch and pop off with pry bar. Number pieces as you remove them so you will know where to put them back.

I found using a 4" drywall knife to pry it up works well. It's thin enough to get under the quarter round or shoe molding and doesn't damage the floor or wood.

I find that it is wise to run a utility knife blade vertically along the seam between the 1/4 round and the baseboard. This will cut/break the bond between the baseboard and the 1/4 round if they have been painted or caulked. I also use a thin bladed spackle knife and mini pry bar to remove the 1/4 round. I place the thin bladed spackle knife vertically against the baseboard and work the mini pry bar between it and the 1/4 round. The thin bladed spackle knife helps to protect the baseboard as you gently pry against it. Some pieces may crack/break, no matter how gentle/careful you are. I always plan on replacing some of the pieces. Hope this helps.
Joe E

Thanks y'all. Cutting the interface with a utility knife / box cutter between the top of the quarter round is a must, not just for painted trim but for varnished ones as well.