Flooring Tile - New tile job. One uneven spot in slab.

I am getting ready to put 12" ceramic tile in a new basement bathroom (about 60 sf). The floor is un-finished, un-sealed, 5 year old concrete with no cracks. The surface is fairly smooth and nicely even, except.

In laying out my tile I found that I have one tile that wants to rock just a bit (just over 1/8" rise on one corner when I press the other three down). That happens on the tile that will be on the foot area of the toilet. It is due to unevenness at the flange and/or the adjacent foundation wall. So, obviously I am concerned about movement.

I see three options: (1) Use extra mortar in this area to compensate for the uneveness. That means using some extra mortar on adjacent tiles as well to make sure things taper to an even surface. (2) Grind the surface using some kind of tool that I probably have to rent. (3) Pour all 60 sf with a self-levelling-cement.

I would like to say I can do (1) but I do absolutely want the job done right. What tool would I need for (2)? Can I remove material easily, or is it not going to work well. Perhaps I need to do (2), followed by (1) to a lesser extent if necessary. I prefer not to do (3) because it really seems to be the only uneven spot on the whole floor and I don't want to raise the floor too much.

So, what do you think?

Thanks, Nick.

PS, surface prep: The surface is clean, but has minor white staining from drywall work, and it is fairly smooth. That's OK, isn't it?

If only an 1/8" in one tile corner, the thinset might just even it out as you set the the tile, you will use a 1/4 X 3/8" square notched trowel, you can also feather out this area with thinset first to even it out or just take a hammer and chisle if you don't have an angle grinder with a masonry grinding wheel on it and chisle and chip the high spot down, don't worry about going to low or roughing up this area with the chisle, the thinset will work it all out, use a modified thinset.:)

No need for SLC if the rest of the floor is fine.:)

Wash the floor with water, it will disolve the drywall crap and wash it away.:)

Thanks Tileman! I appreciate the advice.

I think I will chip what I can and then "feather in" some extra mortar as you suggest. I will give the floor another mopping as well.