Hello,

Yes, indeed Delaminating the document may cause damage but only if you will do it by yourself. There are many professionals who do delamination  of documents by taking some money.You can find them in your local market or you can find some online services that do provide the delamination facility. I am providing you a link below :

https://www.howtoremovelamination.com/howtoremovelamination.html

I hope this helps.