Get rid of the excess P-tex with a blade or scraper, like you would dead skin over a paper cut. It also looks like the gouge is toward either the front or rear of the board judging by the curve of the metal edge - but the pic is too close to tell. Ask yourself if you even need to repair it at all, if it's close enough to the front or rear, it may not even contact the snow to speak of. However, my best guess is that it is a contact point, so something should be done at any rate.
Finally, I can hardly tell from the picture how deep it is. Any girl will tell you, it doesn't matter how long it is, it's how deep it goes that counts.
Anyone here who tells you one or the other option and claims to know for sure is either standing right by the board themselves, or is spitballing. About all I can tell from that pic is you need to cut the excess off and it's not a core shot. Try to post a better pic that shows the depth of the gouge.
Beware of taking it to the first shop you see, they'll usually tell you, 'Oh yeah, that board needs (insert most expensive option).' because they stand to make money off of it. Not all shops are dishonest, but enough of them are that you need to be wary.