Quartz worktops are usually made of reconstituted stone (quartz chips) mixed with polyester resin binders.
It's the resin that burns, causing the mark.
People suggest all kinds of folk-remedies usually involving baking soda or toothpaste.
Maybe Ok for minor blemishes, but in your case, Retro, I guess professional re-finishing is needed. (Not my area of expertise I'm afraid.)
For that reason, I always fit these each side of a hob............
https://www.screwfix.com/p/unika-self-adhesive-worktop-protector-6-pack/39766?kpid=39766&ds_rl=1241687&ds_rl=1245250&ds_rl=1245725&ds_rl=1245250&gclid=Cj0KCQjwyLGjBhDKARIsAFRNgW9Oo_t0CROT2HT8pBhat9AvjHajdzjZmQnilWKo1hJeCoJ_aN7lI4UaAu2UEALw_wcB&gclsrc=aw.ds
I know it's too late now, but possibly.......... fitting them now (over the mark) might be enough to take your eye off the damage.
Sorry I can't be more use.