Hi,
Perhaps a technical point. I don't think redemption could be called a way to restore your opinion of me.
I think of "redeeming as "buying back" something you've given up - as getting something back from the pawn shop.
What is being searched for in the eyes is not the way to redemption, but some indication that the redemption has been successful. (Yes or no.?)
That's the way I think of redemption.
It's certainly possible that the eyes may be searched [periodically] for clues as to the way redemption may be won.