removing starnut
 

inside a carbon steerer tube. can i just drill it out with drill bits?

Yes. I've done it. It's a pain, but you can do it. Expect to have a tiny ring (what is left of piece that holds the stars together) stuck around your drill bit.

Star nuts aren't designed to be removed. Not sure drilling it out would not damage the fibers in the steer tube. Typically when a new star nut is needed the original nut is pushed down further and a new nut installed.

What is the reason you want to remove it?

Most things aren't designed to be destroyed so they can be removed. But it can be done.

First, there should never be a star nut in a carbon fiber steering tube. If there is, then the tube is already damaged. The only exceptions are those with an aluminum liner - Alpha Q and some Cannondale forks, for example.

If the star portion spins when drilling it out, then more damage will be done.

+1, a carbon steerer fork should never use a star nut,
if there is one, don't use the fork, in fact, cut it up and then throw it away,
so no one else will attempt to use it..

an expansion fitting the proper parts in a carbon steerer fork, has a separate method of installing it,
from the nut function to make the headset pre-load function.

in a Steel steerer, with a cane creek star-nut, I have removed those OK..
they are partially aluminum. so pull apart if pulled on hard enough..
the aluminum joins the 2 spring steel stars, and the steel 6mm internal threads.
so the aluminum breaks out from the stars, then the stars get turned sideways
and come out with pliers, to grip the edges ..

I agree: destroy the fork. Weigh the cost of a replacement against an emergency room visit.

Obviously I'm not the one riding this bike, so the OP must make his own decision.

But the starnut is usually in the section of the steerer surrounded and buttressed by the stem, and also by the expansion plug, so IMO. whatever damage might have been inflicted when it was first pushed in won't be consequential. That assumes that it was only pushed in and the scratches are shallow and no effort was made to pull it back up causing a deep score.

Removing it by drilling through the center then folding the leaves edgewise and easing them out with pliers isn't hard, and the OP can examine the fork and judge for himself whether he wants to ride it. Factors he can consider are the depth of the scores, whether they appear to have reached into the carbon layer itself, and where they end with respect to the stem and plug.

Unless there's a narrowing down at the bottom of the fork, as long as the steerer tube is the same diameter from top to bottom, use a long drift to knock it all the way through.

I don't like correcting other posts, but can't let this one stand. Do not attempt to push it all the way through because that will extend any damage the star nut causes down into the critical crown area where the stress is highest and a failure most catastrophic.

If you prefer, you may push it lower by an inch or so to get it out of the way of the expansion plug, and leave it there. Don't go deeper than necessary since there's no benefit, and therefore no reason to make a possibly bad situation worse.

Fork's toast anyway with a star nut in a carbon steerer...

I believe some specialized forks came with star nut (not saying is right ok?) from the factory, as for use a dremel or a drill yes can be done.