if the latter, you could look for tent repair patches: I believe they are either iron on or they can be glued with one of the glue-like products used to seal seams on waterproof fabric items (and they should be suitable for outdoor UV exposure etc.).

there may be a difference of suitable products depending whether the waterproofing on the parasol is silicone based or not

(I know that they exist, and I've used the glue-like seam sealing thing, but not the patches)