Covering the tank shouldn't cause it to overheat, especially if you aren't covering the top. THe water heater should turn off when the water reaches a certain temp and turn back on when it drops, so if the towel happens to insulate it a bit, the water heater just does less work
New turtles can be shy, so if that makes them more inclined to bask, go ahead and use it. If they are getting bolder and will bask without it, then leave the towel down. When I first had my turtle I put cardboard around the end of the tank when the basking perch was so she would feel alone and more relaxed when basking, I think it helped her adjust. Now she basks whenever, whether people are present or not... it was just a matter of her getting comfortable.