There are a number of places on the e46 where BMW did not take the trouble to make the car as easily serviceable as they made the e36. They did not drill holes in the e46 beneath the roundel pins to make it easy to remove the roundels without damaging the paint.
The roundel is held in place by two smooth pins that press into rubber gromets that snap into holes in the hood.
Try to slide the corner of a credit card beneath the roundel. If it is too tight, try dental floss. Once you have lifted it just a crack, you can use the credit card to protect the paint while you pry up with a small sharp flat blade screwdriver. Work slowly and patiently.
The new roundel just presses down into place. You probably want to use new rubber grommets. They are cheap.
Avoid spraying your new roundel with high pressure car wash spray.