I don’t know about “chalk” but vinegar dissolves most hard water setements.

Fill a plastic baggy and tie it around the faucet so it’s summerged in vinegar. Use like an old toothbrush on it every couple hourswhile letting it soak for a while and it will all come off.

Now that that’s gone, try the old methods to remove the plastic piece

If you still can’t you have 3 options:

1. Demolish it, it’s plastic and the parts staying are metal, rip it to shreds with pliers.

2. Use a strong adhesive like super glue to glue something to it, wait for it to dry then unscrew it.

3. Call a plumber

You could also just replace the whole faucet, at a certain point that’s just easier.