I notcied that one of my gutters developed a hole in it. What is the best way to patch the hole in the metal gutter? Thanks

My house is surrounded by many trees and has a very high pitched roof. We have installed a type of gutter guard over the gutters that is a hard, white solid plastic that completely covers the gutter except for a small water drainage hole. This works to keep out leaves, nuts, etc., even though rain overflows during heavy downpours. These were quite expensive compared to the screen type gutter guards. The problem is keeping them on the gutters. Over half of them have blown off, even though we lifted up the shingles and hammered the gutter guards up under the shingles. They appeared to be secure. We would like to nail or screw the gutter guards onto the plywood under the shingles to keep them on the gutters. Are we risking making the roof leak by nailing or screwing them into the roof? Should tar or caulk be used over each nail or screw? Any advice you can give is greatly appreciated. Thanks.