After removing as much as possible, the grinder might be a good option. It would also roughen the surface of the concrete, giving the paint more "profile" on which to adhere.
If this concrete is in contact with the ground, I strongly advise you to use a special primer meant for below grade concrete. It will help keep moisture from migrating through the concrete over time, keeping any metal or wood parts of the furniture from being damaged by that moisture.
Good luck !