Your ultimate solution depends on the source of the "grinding".
Is it constant or sporadic depending on the gears selected? Does it stop when the pedals are not turning? Does it stop when the wheels are not turning? Is it coming from the crankset/chainring area or the rear hub/cassette? Or neither?
If the chain is rubbing against the front derailleur cage, it is probably an adjustment issue. If the chain is "chattering" between cogs in the cassette, it is probably an adjustment issue. If you paid a shop to remove the "grinding" and it is back, then a reputable shop will most likely reinspect it and make the adjustment(s) as part of the original servicing.
If the grinding is due to worn components (most likely a worn chain or cassette or aging cables/housings), then the shop should have called that to your attention prior to servicing. In that case, you'll probably have to pay for replacing the worn component, which may or may not require readjustment of your drive train. Whether readjustment will cost you additional expense depends on the shop. It wouldn't be abnormal for a shop to make basic adjustments for free when installing a new cassette - especially if they had just performed a tune up. If the shop called your attention to worn components and you elected not to replace them as part of the servicing, then you kind of have to "take your medicine". Still a reputable shop would most likely replace the component and not recharge for a "re-tune"
If the "grinding" is due to grit in a bottom bracket or wheel bearing, then a reputable shop should have identified and fully serviced the bearings. Grinding could also be caused by grit imbedding into your brake pads - which you would hear only when braking. There are so many possibilities and definitions of "grinding" that you'll have to be a bit more specific to get corrective input from an internet fourm.