I am using plasma etching system with mixture of Oxygen and Argon as 1:1 ratio with power 100 watt for 30 seconds.

To my opinion, it would not change much...The etch rate will be determined by the power (which is pretty high here given you wanna etch a 1 atom-thick layer).

I guess you want to get rid of the graphene on the backside so that you can transfer graphene present on the top side, right?

Option 1) The top side of your foil in the plasma reactor will be etched faster given that it is in direct contact with the plasma/radicals. It is more difficult for the radicals to diffuse underneath the foil and etch graphene on the backside. If your sample is big enough (>2 cm), you might be able to save a bit of graphene from the center of the backside while having the top side totally removed...Still a pretty bad option as your graphene in the periphery will be damaged....especially for a not super flat Cu foil.

Option 2) You coat your good graphene side with PMMA (or PC, PS, PDMS, or whatever photoresist you have access to and which is easily removed in solvents). If it is thick enough, it will protect your good graphene. For the transfer, you need that polymer mechanical support anyway...if not, remove it with a solvent (acetone+IPA rinse).

Option 3) You coat the good graphene side with your polymer and start the transfer process. While the bad graphene side is sitting in the Cu etchant, the Cu is going to be under-etched via percolation of etchant through graphene cracks/wrinkles/defects. You don't want to get the bad graphene to crumple/wrap on itself so you pick your Cu/gr/polymer with your tweezers and dip it in a separate DI water bath to detach the small fragment of graphene (don't hesitate to shake it well) and then put back your sample in the etchant. Replace your dipping/rinsing DI water bath and repeat that 2 more times with a 2-3 min interval (to let the time for the Cu etchant to further etch and detach graphene). In that way, you can be sure that all the graphene at the backside has been removed and you get a clean/uniform Cu etching. Personally, it is my favorite technique...no need for plasma equipment, just a bit of FeCl3/APS.