Now that the pads are removed you will need to move the pistons in the caliper back so that the new, thicker pads will fit in.
First, you should remove a bit of brake fluid from the system. As the old pads wore down, there was room for more fluid in the system and the level was likely topped off. With the new thicker pads in place there will be more fluid in the system that there is room for, potentially.
Begin with this process by removing the cap on the brake fluid reservoir.