Gap Between granite and backsplash- what can I do?

Where and what material is by this gap? Non sanded grout is good for most gaps and comes in many colors to blend in. Post a picture from farther away please.

Could you be more specific in your question? How large is the gap? Is it on the wall, or between the granite and wall? A picture might be helpful as well...

I would buy white/ cream /Black rope tile trim.

Grout is no used between countertop and wall tile. Caulk (normally used) would not work because it's too large a gap. Darciegage2 has the best solution. A pencil tile trim would cover the gap. Big box stores have them.

https://www.google.com/search?q=pencil+tile+trim+home+depot&source=univ&tbm=shop&tbo=u&sa=X&ved=0ahUKEwjUm_6JnZ7ZAhXE24MKHYrDDnIQsxgIKA&biw=1016&bih=642

Looks like you had a new counter installed. the old counter was thicker. I would ask the granite counter guys to provide you with 4" back splash that could be applied to the tile splash, which I see got damaged

I would fill gap with a piece of tile trim. Home depot, tile stores have beautiful trim pieces and applying a trim would give your projuct a finished look.

A piece of wood trim painted to match and cut to fit.

You could use a Ceramic trim or Plastic or Gap Filler used in bathrooms, or Timber trim or mini tiles. etc.

Caulk is a potential solution: https://www.youtube.com/watch?v=ZMAc9FlshnM

According to this article you could also use some kind of wood trim: https://www.hunker.com/13412445/how-to-cover-an-unattractive-gap-between-a-granite-countertop-a-tile-backsplash

How wide is the gap?