The "ink" is a roll of foil covered with color sheets and its size covers 100% of the paper. If the paper size is smaller (like credit card size) the 10x15 ink will be too big so either it won't work or will mess up with the colors (as it will not roll far enough to reach next color).

Use the ink that is provided with the paper accordingly.

It is safe to remove the ink cartridge anytime and not only at the end of the roll.