Scrape, fill, prime, paint.

Scrape the raised area with a razor blade. Block sand it with 80 grit, hitting more than just the bad area.

Cover with a thin coat of wood filler, using heavy pressure to force the filler into the fibers. Once that dries, block sand again with 120 grit, then once more with 180 grit. Make sure you sand beyond the patch to blend the repair into the rest of the sill.

Thoroughly clean the dust. Apply two coats of primer to the full sill. Once dry, sand lightly using 220 grit, without a block.

Clean up any dust, then paint.

You'l have a smooth sill with no signs of damage.

It will depend on the material under the paint. Any particulate board you will probably want to replace. Wood can be dried, sanded and repainted depending on the depth of the damage.

But you will need to check the state of the material under the paint to know for sure.

Edit: looking closer at the picture it looks like melamine maybe? If that is the case you should replace it if possible.