I don't keep screens either. If I happen to have screens still on press I'll do another shirt at the per-piece price and explain to the customer that it's because the job was still set up.
I don't charge for screens, I charge for press set up, which includes burning the screens, taping, and registering the job. This makes it easier to answer the question we've all been asked: "Why do I need to pay for a screen? You should have it from last time."
As mentioned in other posts, if it's just a spot, why not gun it out? If it's a spot within a print, you'd be surprised how well you can touch it up with a screwdriver or a toothpick, ink, a paper towel, and a little patience. If you repair a spot and it looks lumpy, your heat press and a piece of kraft paper will take care of that.
All that being said, if it really is something you did wrong and the shirt needs to be replaced, I'd bite the bullet and print a new one at no cost. It might be annoying but will pay off in future orders and word of mouth advertising. I'd also politely ask the customer to please inspect future orders upon delivery and let me know if there's a problem within a few days.