Can I cover Brick backsplash? Or must I remove it?

Hi Kay, it is lot less physical work to paint the brick than to remove it, and you can always change the colors over the years.

https://www.youtube.com/watch?v=ZZLj9m39Qr0

Painting is always less work then removing brick. If you don't like the look of paint you could white wash it and that would still allow some of the natural variations in the brick to show thru while giving it a face lift at the same time.

If your brick and mortar are in good shape, I would consider painting it, if you are tired of it and want a backsplash, the brick has to either be removed or mortar filled in to attach the drywall.