Can't tell what kind of tile just by looking at a photo.

It can be gotten up with a chisel and/or jackhammer. It's nontrivial. What's that drop-down in the first picture?

You might be able to lay something over it if it's level, either a vinyl plank with some padding attached or a carpet with some underlayment. If you're demoing the whole basement and aren't short for head clearance, that might be a better way to go.

ACM - The drop-down in the first picture is the "unfinished" part of the basement where the washer and dryer are, the water heater, etc. I can't figure out why the basement has flooring that is two different heights. We are short for head clearance on the "finished" side where the tile is .... it's only have 6'5 which is why I was hoping we could have the tile removed and keep our drop-ceiling b/c we do have a lot of stuff running through the ceiling that I don't really want to cover up completely.

The painted floor is the bottom, concrete from when the house was made; when they put tile down, the thickness of the tiles and the thinset base account for the differences in height.

Thanks! So if we remove the tile, will the floor then be same height as the floor in the unfinished part of the basement?

that is indeed, red quarry tile. you might be able to get the entire thing refinished and looking like new. it's nice when it's all cleaned up and spiffy. It also came in black (blue quarry). maybe you could get them recolored and polished?? not sure

I would look into getting them refinished as an option. they look nice when completely redone.

as for the height diff, the tile is set on top of what looks like a higher plane. so unless you jackhammer all of the cement under it, I don't think just removing the tile will level it for you. And removing all that quarry tile is a big, messy job!

That's what I was afraid of... I'm sure its a very big, messy and dusty job! I really don't like it at all so I'm not sure I would pay to refinish it. Do you think it would be okay to put carpet on top of it?

wall-to-wall carpeting that is... with padding.

I don't see why not,, in a basement. they need to put down tack strips but I'm sure they could attach them to that tile. check w/the carpet company and see if they'll do it. if you want extra thick padding, you have to tell them so they can recommend the correct carpet for it.

If you choose to install carpet over the quarry tile please bear in mind that you will ruin the tiles around the perimeter of the room. A very strong adhesive will be needed under the tack strip and you will need to ensure that said tiles are bonded to the subfloor very good. If the tiles are not bonded properly they will break loose when the carpet is stretched into place, causing big problems for your install.

Skim the grout joints flush and install carpet & pad using the double stick method. With proper carpet & pad of course. This eliminates all that labor that has been discussed. Just a tile guys opinion.

quarry tile when bonded properly come out in bit chunks and leave behind a mess that needs to be mechanically removed or screeded over. Dont take demo lightly

Some carpet guys use small tapcons to attack their tackstrip , but those tile are brittle, I would remove them.

One other thing to keep in mind--how long have you lived in your house? In our former 1950's house our basement was dry for a good couple of years--until a big rain storm, when it suddenly was not dry. Ditto for our current house -- dry except for 2-3 occasions over the last 8 years... Not a big deal with a hard floor, but would have been painful with carpeting. Although perhaps you have a sump pump?

No rip-up, No tack strip. Just skim the existing quarry tile and glue down commercial carpet with pad or without. No need to redo all the base board & possibly door trim as would be required if you rip out quarry tiles.

Carpet tile. PSA. Done.

Or snap lock vinyl with some thickness. Like CorrTec. That would be waterproof if you do have a water event.

Judging by the picture if you did a commercial grade carpet you may be fine but if you add pad with it your doors may not clear, quarry tile is what 3/8? And a 3/8 notch before being set, so 5/8 at most.New pad and thick carpet without the commercial feel would probably assume the gap.

Another option - a quality carpet store should be able to make a custom "rug" for your space by adding binding around the edge of the carpet, and not adhering it to the tile in any way. You could even leave a space of say, six inches, of the tile showing around the edges. They should be able to make it in any shape and size you want.