Lowering the water level below the skimmer will not hurt the liner. And, if you have to lower the water level below the skimmer to install the thing, then you don't need it because once the water level is below the skimmer, your skimmer is not in danger of being damaged anyways. Damage occurs whenever there is water in the skimmer that freezes.

Is this cover something that is installed every fall and then removed every spring? If it were me, I'd take it back and save my money. Just lowering the water level below the skimmer and returns is sufficient to keep anything from being damaged. Just my opinion.