huh? ... "extrude it outward"?

If the goal is to make the rim "thinner" just grab the inner edge and translate it towards the outer edge.

No need to "extrude" or to "scale". But I am sure I am misintrpreting what you are trying to do.

1. create a cube
2. select the top face
3. extrude the face evenly in the xz plane
4. extrude the same face in negative y

you now have a square vessel

5. select an inner edge at the "rim" and translate it in the xz plane towards the outer edge and bingo you've thinned the rim on one side.

or alternatively select the inner face and just translate the face and the entire side of the cup will be thinner on that side.