I dont think you will have any problems tiling over them if they are solid, I would still remove though, for all the work it wll take!!
Charlie if he gets a SDS and rips them up + causes massive vibration to the floor + knocking ceiling down below + causing structural damage to floor/building, it is quite a bit more work than tiling 4 or 5 m2 of tiling.
If they are that solid, and most folk on here have had jobs like this, prep it right it will be fine