an easy fix would be just to clean that up and put grey grout. Another way would be to use those metal divider things. (i forgot what they are called) But that would involve taking off some tiles so it can go underneath. I found a picture when i googled tile divider. looks like the one in the picture. There are many different thicknesses and it would raise the beige tile level with the grey.

or you can use something like this

just put some grout in the gap and push this in it.

This should have been addressed before the install was complete. Rip back the last row of grey tile and install a schluter strip. You need a ramped one, this one is a Reno. It should be placed under the grey tile and will ramp down to the level of the beige one, hopefully eliminating the height difference.