I think it's comparable to someone who is in a loving marriage, but cheats on a spouse. Lets imagine your friend was happily married but made a mistake and got into an affair. Imagine she thought her husband would leave her, but to her shock he stayed with her, and he told her "I love you so much, I'm forgiving you for that and I want to have a complete marriage with you again."
Would her response be "Okay great... you're forgiving me.. so I will continue on in this affair seems how I have forgiveness for it"?
Well, it shouldn't be. Her response should be that she is so overwhelming grateful at having a second chance and having her mistakes forgiven, that she'd instantly stop the affair and break off contact with the person she was having an affair with and she'd give herself fully to her marriage.
I think that's how we should respond to God's grace and forgiveness with our sins- not thinking that we have a 'free pass' to sin, but rather being happy that we've been forgiven and using the opportunity to make a clean break from our sins and serve God more fully than ever,