How do I get these smudges off my wall?

I have had this problem before and got it off successfully with an Enjo mitt and their marble paste. If you don't have that, try some kind of powder-based cleaner and rub really gently. In Australia I would recommend gumption. Whatever you try, you will need to patch-test it on an area to make sure it doesn't mark the paint. You haven't said what kind of paint is on the walls, so I'm thinking it might be matt. If it is gloss then you have a bigger problem.

One other thing to try on gloss paint (and patch test it first too) - put a small bit of vegetable oil on some cotton wool and gently wipe the area. I've used vegetable oil to get some fairly dark tomato sauce stains of white plastic and it just seems to lift them really well. It might do the trick for you. Good luck.

Try using baking soda and a very damp, not wet, rag. Dip the rag into some baking soda and very gently scrub the marks. It should start coming off. Reapply the baking soda as needed. When you're done, wipe the area with a different clean damp rag to get the baking soda off. Hope this helps. Good luck!

I had a similar thing but it blue and transferred by continuous contact with the wall. Greased Lightening is a good chemical cleaner that works for lots of things. Bleach and water would work.