Have to removel old TIM as just plooping a new cooler on top will create air bubbles which ruin the heat transfer. To remove it i wipe most of it off with a paper towel before finishing it off with a paper towel soaked in white spirit or meths.
Definitely clean the old off first and reapply. In the past I've just used a cotton bud dipped in the gf's nail varnish remover - seemed to work ok... Sent from Bittech Android app
Turn the PC on first and run something like prime 95. it will soften everything up and should come off easily