Forgive and forget
Definition 1 of 2
Pro Tip 1/3Sincerity Matters
Using 'forgive and forget' implies true forgiveness, without holding grudges or negative feelings. 
They shook hands, promising to forgive and forget past disagreements.
Pro Tip 2/3Full Resolution
'Forgive and forget' means resolving an issue fully so that it's as if it never happened. 
After a heartfelt apology, she decided to forgive and forget.
Pro Tip 3/3Not Literal
It's an expression; forgetting completely isn't always possible, but it's the intention that counts. 
He said he would forgive and forget, even though some memories are hard to erase.