If you replace the anchors with new ones, make sure they are the same outside diameter, otherwise you'll have to drill or fill and then drill new holes.
Removing the old anchors is easy - use the existing posts to pull them out. Make yourself the tool pictured below from some scrap wood and then lever the anchor out with a claw hammer or similar. You can just see mine has some foam rubber tape on the bottom to prevent marring the finish on the guitar.
The one thing to watch out for is body finish overlapping the anchors - if they were pressed in before finishing, the finish overlaps the top of the anchor and it can chip the finish around the posts when you pull them. If you have this, clean the finish away from the anchors before pulling (I use a Dremel, but you can use a blade or small chisel - score the finish around the anchor so it chips away where you want it to and chip away...).