Hi,
to remove the gaitor it depends which type you've got...
i've got the 'older' one where its just a piece of 'leather' so all you do really is just reach in and pull it out... lol i know its a bit vague
look at that video,
i would NOT do what he did with the card though, you risk scratching the plastics and removing that soft grey stuff VW put on the plastics. just reach in and pop it out! its the same procedure for both the leather only and the one where you've got the silver stripe
what exactly is the problem you're having with it?
i've changed out my gear oil, lubed up gear shifter mechanism, changed out the boden cable catches (those black plastic catches at the gearbox end) adjusted the gear linkage and i've still got a slightly notchy gear change .... but my mileage is juuuuust about to touch 158,000....lol. so its probably just my gearbox showing its age.
depending on your mileage it may just be a sign of its age and you'll just have to live with it unless you really want to recon your gearbox - a bit overkill in my opinion but if you want it to be absolutely perfect then its your car and if you want it that way then make it so!
stick to OEM gearbox oils, stick to OEM greases for the mechanisms... they're mostly designed to last the life of the car - VW actually say to never change the gearbox oil - thats how much faith they put in their gearbox oil!