You're editing only the logo drawn on the big helmet. The shell and facemask show faintly as a guide and aren't changed here. Nothing touches the ROM until you click Apply logo.
Why a logo might not fit. The NES draws the logo from 8×8 tiles called sprites, shown as yellow boxes. A helmet has room for about 20 of them, and only 8 can sit side by side on one row. Boxes stay where they are. Pixels you draw outside every box get a new box. To fit, keep the logo compact and avoid wide rows. Moving boxes so they line up or overlap less can also help, and Auto-arrange sprites lets the editor choose the boxes again. The original 28-team ROM also has little spare tile space, so changing pixels inside existing boxes fits better than adding new ones.
Using another paint program. Export PNG saves a 72×84 picture with a transparent background: the logo on top, and a strip below with blocks for colors 1, 2 and 3. Edit it, keeping the size and position, then Import PNG….
This edits the small helmet on the team-select grid by changing the pixels of the graphics tiles it is drawn from. Nothing touches the ROM until you click Apply.
Using another paint program. Export PNG saves a 24×36 picture: the background layer on top, then the overlay layer, with a transparent backdrop and this helmet's own colors. Edit it keeping the size and position (a scaled-up copy also works), then Import PNG…. Each pixel snaps to the closest of the layer's three colors, so draw with hard edges and no smoothing.