How do I clean eggshell painted walls?

You’ll probably have to repaint.

Ask Angie: Be gentle when cleaning eggshell paint walls | Lexington ...

https://www.kentucky.com/living/home-garden/article44503206.html

You can also use Mr Clean Erasers but be careful if you scrub too hard, it can remove the paint and here is another idea

How to Clean Eggshell Paint Walls | HOUSEHOLD TIPS & CLEANING ...

https://www.pinterest.com/pin/1548181099340296

I would wash them down again using just clean water to see if that helps. Perhaps you still have some soap residue.

Hate to say this but it sounds like some of the paint was removed and that means repainting. For future reference try using a Magic Eraser and be gentle. Our walls are a satin finish and seem to hold up a little more to cleaning.

I wouldn't use dish soap to wash the walls it sounds like that in combination with the vinegar could have eaten away at the paint. Definitely try just using water.