Brake pad replacement

The cap on the reservoir seals it to keep out air with the humidity in it. As the brake pads wear, the pistons work their way out of the calipers to self-adjust. Brake fluid fills in the space behind the pistons, and that fluid comes from the reservoir. The rubber bladder seal under the cap extends to prevent air from having to enter the reservoir.

When you pry the pistons back into the calipers before you remove them, that pushes the brake fluid back up into the reservoir. That is why we never top off the reservoir during other routine services such as oil changes.

You are referring to pumping the brake pedal to run the pistons back out so the pads will contact the rotors. You are going to pump the same fluid out of the reservoir in a few seconds as would normally come out over time as the pads wear. The bladder seal is designed to extend out of the cap to prevent vacuum from building up, so no, you do not need to remove the cover.

What I suspect you are about to do is a real common do-it-yourselfer mistake. That is pushing the brake pedal to the floor multiple times. Crud and corrosion build up in the lower halves of the bores where the pistons do not normally travel in the master cylinder. Pushing the pedal to the floor, whether to run the pistons out, or when surprised by a sudden leak, runs the rubber lip seals over that crud and can rip them. That results in a slowly-sinking brake pedal, and that often does not show up for two or three days. To reduce the chances of this happening, never push a brake pedal more than half way to the floor unless the master cylinder is less than about a year old.