Lee, You weren't specific with dimensions, so I will give you an idea in a general way and you can figure the details for the specific requirements of fit and finish. Obtain a suitable wire mesh that meets your specifications and mechanically fasten it to the Luan. This will not be objectionally thick and will offer a good porous surface for your mastic of choice. Be sure to check your depth behind the backsplash when determining fastener length. You need to know if there might be wiring or ducting and just how far the outside wall is separated if at all!!

Ask a Pro, hire a union worker, they do it right.

JIM