Adjusting eye relief after scope is already mounted?

I had my scope mounted when I ordered my pcp. Zero is dead on, scope leveled right and works great. Only issue is it's a tad too far back for proper eye relief in my natural cheek weld position. I have to move my head back a bit and it feels awkward. My question is can I loosen the mounts and slide it forward or do I need to loosen the scope in the rings and adjust? I don't want to mess my scope up but being able to just adjust the mounts forward would seem like it would avoid messing up the scope being level. 
 
If it's mounted on a picatinny or weaver rail, and you have a set of forward slots, that would be easy. Just take out the cross clamp screw all the way and slide it forward to the next slot. If it's on a dovetail you only need to loosen it up and move it forward.

Be sure your final position is made with the scope on it's highest power as that's when eye relief problems show up.