Mounting is necessary to give the rubbing a more substantial support than a single layer, but you don t want to flatten it out completely as you would with other ink-brush paintings because the images in the rubbing may distort and become out of shape if the paper is stretched flat. So wet mounting a rubbing is a very delicate job. Now, if I understand you correctly, you have a rubbing that is glued to the back of a window mat. Your immediate concern is getting the art separated from the existing old mat. Without seeing the actual thing, my suggestions are based on assumptions only.
Chances are that the glue has penetrated the rice paper.
If the paper is a high bark content, your job would be easier. Rubbings from South China or Asia like Thailand and Cambodia are usually done on bark papers. Rubbings from Central and North China are usually done on the thinnest rag Xuan called mianlian . If it s one of those, you need to have the patience and caution of an eye surgeon to remove it from a glued board. That s if the glue is water-soluble.