Hi,
Here is a link to the service manual for a Dell XPS 13.
http://topics-cdn.dell.com/pdf/xps-13-9350-laptop_Service%20Manual_en-us.pdf
It shows that the hinge screws screw into the palmrest assembly. It seems as though the threaded screwhole(s) may be stripped. Most likely you will have to replace the entire palmrest assembly.
If you scroll to p.82 in the manual it details the necessary pre-requisites and then the procedure to remove/replace the palmrest.
Here is a link to some suppliers of the palmrest assembly. It is not a recommendation to buy from them. It is shown just to give you an idea of the cost of the part. There are others online that may suit you better.
Also to ensure that you get the correct part, in laptops, notebooks etc., usually the part number is stamped on the underside of the component (part). If you search online using just the number you should get results for suppliers. Obviously you would have to dis-assemble the unit to remove the palmrest to see the number.
http://www.ebay.com/p/dell-xps-13-ultrabook-palmrest-assembly-w-touchpad-1rv06/1200239790
Hopefully this is of some help.