The service manual states to place a wide, thin blade putty knife to push the pistons back in. Doesn't mention to take the brake reservoir cover off.
If some topped of while the pads were low it is possible to overflow the master cylinder. better to remove the cover and remove a little fluid then compress pistons replace pads then press brake lever to seat pads and top off if necessary
I use thin wooden shims (the kind you would square a door/frame with), one from each side of the pad, to push the pistons back. Works like a charm and no marks on the rotor. I also remove the master cylinder cap.
Put some clear tubing on the bleeder nipple, crack it loose, and let the dirty fluid go that way instead of back into the master cylinder. Leave the cover on.
I started using these several years ago and they are the best. Make bleeding or flushing (changing) the fluid a simple task. Be sure to buy the hose and bag with the bleeders you need.