Okay, if you're going to do it:
gently remove all the spagnum you can with your fingertips then rinse away any that is left with clean water. If you want to use the same pot, clean it well (I use a bit of bleach and hot water), then repot the plant into your new mix. Never ever re-use any potting medium unless you are using aliflor or PrimeAgra --- but that's a different lesson
When I repot, I never push the medium down into the pot. I put some in, then the plant, then hold it in one hand while you add more...then tap the sides of the pot to allow what you've added to drop down into the spaces available. Pushing down can damage the roots...it's okay to gently handle the roots but squashing them into the pot would be a no-no
Water thoroughly...
let us now how it turns out