Is there any way to reduce the negative effects of an mri on the knee after a knee replacement?

Not true: there are no effects on a knee replacement from having an mri scan

There aren't: any negative effects!

Timing: There is a general thought that there may be a subtle vibration in the joint replacement which might potentially lead to a loosening of the implant, particularly if it is a device that requires bone ingrowth for stability. So there is a 6 week time frame some will wait before getting an MRI. That being said, I have never seen any problem with getting an MRI on a patient with a replacement.