In a pickle...need your thoughts.

In late May I was hired full time as a graphic designer. I only worked at the agency for 3 weeks, and resigned because I didn't feel like I was a good fit.

So, during my time there, I only worked on one website and finished as much as I could. I left the rest of the work to the other designer. Now, they called me back the other day because there was a bug and couldn't figure it out.

Should I debug it free of charge or charge them my hourly rate?

Hourly rate, you are under no contractual agreement to support any bugs. Since you were hired full time, all the work you did there is owned by them, and therefore their responsibility to have fixed.