Goggle anti-fog coating appears scuffed / how to fix

Hello, I'm new to swimming properly. I messed around with a poor breaststroke from childhood until October last year, when I decided to start learning front crawl. I've done quite a bit of snorkelling, so when I committed to learning to swim correctly, I favoured a mid-size swimming mask instead of goggles...I just found this more comfortable and I never had fogging issues that a good dose of saliva wouldn't fix. A few weeks ago, I decided to try the Arena Pure goggles for a change. They are supposed to have an anti-fog coating, which should never be touched by hand etc etc. On their maiden outing, I just couldn't get comfortable with them and I thought they were fogging up, so I employed the primitive method (rub saliva into the lenses with finger). You may well slap your foreheads at the stupidity of this, but I felt I had to try. The result was a smudge at the centre of the lenses. When I got home, after rinsing in fresh water, I decided to wipe the interior with a soft microfibre cloth. The result is that the centre of the lenses appears scuffed and visibility is reduced. I don't think the lenses truly are scuffed, unless the lense material is absurdly soft. Yesterday, I applied some Cressi Anti-fog in the hope that the layer may recover and the interior return to its original condition, but it didn't work. The lenses look as if someone has rotated a scouring pad on them. I guess I should remove the remainder of the original anti-fog layer and just reapply the Cressi solution, but I'm not sure how to remove the original layer without damaging the lenses.... Can anyone please advise? Many thanks in advance