Gamvar tends to remain somewhat tacky for quite a while. If it is applied too thickly it will never dry, so make sure that it is not at all tacky to the touch before you put anything over the top of it.
The best material you can use in my opinion as a cover sheet is silicone release paper, the type that is used in heat mounting art and photography in a dry mount press. It is the ONLY cover sheet I would use on Acrylics. A fully dry oil painting may not really need it but it is good insurance against the customer receiving the painting with something stuck to the face of it. You can buy it from several sources. This material is also recommended by George O'Hanlon.
Better than having something in contact with surface is to package it in such a way as to have the front of the painting suspended with nothing touching it.
Some artists will remove the painting from the stretchers and roll it to ship it. Personally I would only roll acrylics as rolling fully cured oils can produce micro-cracking that can develop into visible cracks later..
A decent method from Draw Mix Paint. There are other methods that also work well.