I think that maybe a white subway tile would look nice and could run up to the bottom of the hood. You could also do a accent above the range with a pencil tile maybe in black to tie in the granite with a simple design inside the framed pencil area.

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Adding another portion to your backsplash may create a choppy look and visually shorten your wall height that could make your kitchen space look smaller. You have good, clean lines that can be enhanced with simple paint color. Using a good washable kitchen and bath paint will work fine. This will help break up the black and white look of your counter tops and cabinetry. It can also help "pop" your space and tie together your flooring as well into the picture. And it's less costly than the tile route.

A few things to consider if you choose to add tile: the total thickness so that it doesn't exceed the current backsplash thickness, outlets and cover plates may need to be adjusted for tile thickness, and the framing areas for the backsplash should not exceed the bottom portion of the cabinets. The stove back already is taking up considerable space. It would look unbalanced and busy to use tile behind it. Hope this helps. Thanks.

Your beautiful kitchen can be bright and cheery with a colorful rug, towels, curtains, toaster cover ( :) ) etc. A backsplash is not needed.

If teal is your color, it sounds great, especially with white and black with your wood floors. Paint all the way up to the ceiling...all walls. Leave the ceiling white as is which will make your walls be the "accent" in your kitchen. It will keep it bright and cheerful. If you ever tire of the color or it becomes dated, just repaint. It's timeless.

Removing the granite backsplash shouldn't be too hard and, if there were any damage left, most likely it would be minor and easily patched. The only issue I'd be afraid to uncover would be if the installers didn't have the counter top squared correctly to your walls during fabrication and the backsplash is actually covering some wide gaps along the wall. If there are any gaps, hopefully any new tile will be thick enough to cover them. I personally would tile the stove backsplash all the way too. These are always neat areas to be creative with inserts or designs.