There are special tools you can buy to help with removal and replacement of GU10 bulbs, like this one:
https://www.amazon.co.uk/Small-MR16-...dp/B008HSPLVU/
(Other suppliers are available)
It's a suction cup with handle. It sticks to the flat front face of the bulb, allowing you to turn the bullb in the fitting and pull it out. Often the bulbs are recessed inside the fitting, making it difficult to get a good grip with your fingers alone. The suction cup gripper solves the problem.