You surely can forget things that you don't ever deal with. Most experiences fade into unconscious archives without much analysis or resolution. Likewise, you can forgive faults that still occupy your awareness. So forgiveness and forgetfulness are not simple synonyms.
I put forth that once you have forgotten a grievance you can no longer forgive it. To match the phrasing of the original expression, you can't forgive what you have forgot. Forgiveness isn't when problems go away. It isn't when the offender makes restitution. Forgiveness is a deliberate pardoning and letting go of desires for retribution. It is the expanding of the soul. Forgiving is therefore impossible after forgetting. Forgiveness will remove the sting from remembering and render our memories complete.