Peter found it hard to grapple with the idea that the degree or amount of sin was irrelevant. But " seventy times seven" indicated how far out he was. Even when a brother's repentance seems humanly unlikely (the 490th time in the day takes some believing!), we must still have that covenant mercy for him. Note that only a verbal repentance was required- and the Lord said that the forgiver was to just accept this, rather than demand evidence of 'forsaking' in physical terms. The Greek word for repentance is a compound meaning ‘to think differently after’. Repentance is essentially a changed attitude of mind. This is why it’s difficult to judge whether it exists within the heart of another person. Because our very natures are sinful, we live constantly in need and receipt of mercy, every second of our existence. The New Covenant is often spoken of in the Old Testament as " mercy" and/or " truth" . If we are in that Covenant, we are permanently living in grace/mercy. Mercy is not something which we just receive in the few moments while we pray for forgiveness. It is something constantly ongoing. We live in it. If we appreciated this, we would not see our forgiveness of others as something we occasionally 'grant'; we will extend mercy to them constantly, as God does to us.
Some seem to think that we only occasionally sin, and then we repent and receive mercy. This disregards our innate sinfulness, and the nature of covenant relationship with God. We are still in covenant with God even in the midst of our sins, as Israel were until the covenant was broken. Likewise, Mrs. (Sis.!) Bloggs is still Mrs. Bloggs at the height of her screaming argument with Mr. Bloggs. It is not for us to eject others from God's covenant. All we can do is to insist on adherence to certain basic doctrines which comprise that covenant. Any who reject the doctrines which form that covenant must be ejected from fellowship, because they refuse to accept the nuts and bolts of the framework which makes up the covenant. But for someone who is in covenant with God, we must show them the covenant of constant mercy which God does to us.