I accidentally damaged my gigabyte eagle rx 6600 upper side edgs connector during installation,a capacitor named 'C25' is removed,but the card is currently running fine,Is it a major issue?
Its a Gigabyte card it was damaged when it was made. You will be fine.
Chances are it's a filter cap meant to give AC noise a path to ground while blocking the DC component from being lost. Will it "run fine" with it out of the circuit? Most likely yes, BUT it will not run as intended and engineered. Ideally you'd want to replace the pads IAW IPC 7711/7721 and then install whatever the original cap was rated for. Remember you have a lot more wiggle room on the voltage rating, so long as you at least meet the old value you can exceed it, than you do with the actual capacitance value. Far as where to find the value for that cap? Get creative my friend.
Dan,
Second Chance Repairs LLC