Since the covering is often not attached as well as it could be, and is sometimes wrinkled, consider buying a covering iron, and perhaps a heat gun. The iron is needed for sealing loose covering edges, and can also be used for shrinking the wrinkles. The heat gun is better for shrinking, since it can cover larger areas. However, as has already been mentioned, don't use a heat gun near the edge of any piece of covering or trim, it can turn a straight edge wavy.

One more note, don't fuss too much over your trainer. They usually go through plenty of minor mishaps as you are learning to fly.