Your challenge is flawed. Does your wife see you as the righteousness of Christ? Does she see you as perfect and never remember your sins? When your wife looks at your does she see Jesus or you and all your faults?
Your relationships must be a mess then, especially the one with the Lord.
So, let's see, you, jzeidler, offend your wife, you know you did, because you have felt the convicting power of the Holy Spirit, your wife comes back with, 'hey, jzeidler, don't sweat, hon, cause, you're a Christian and you can offend me any time you want.' Is that about right, jzeidler?
How about if it is the other way around? Do you say the same to her?
What makes you believe that when you feel the convicting power of the Holy Spirit when offending God, it is Him telling you 'hurray, jzeidler, way to go. Don't worry about the convicting power of My Holy Spirit.'
Is this how you understand the convicting power of the Holy Spirit, it is OK with Him and you don't need to do anything about it?
Besides, I believe the verse that came to your mind has to do with sins that have already been confessed and forgiven, that being the case, the Lord chooses to forget them.
Could you provide the verse in the Bible that says, 'when you feel the convicting power of My Holy Spirit, don't sweat about it, it's nothing to worry about in the least, I, God, just didn't have anything else better to do'?