New Bunny! How to clean oil off of her?

Hi all!! I haven't been on this forum in awhile (it's been a hectic last couple years), but we just got a new bunny. Her name is Mabel and my mom's boss found her as a stray. She was outside for at least a week before they caught her last night. We went and picked her up today because they didn't want her going with animal control. She's very docile and not underweight. She's been drinking and eating hay, pellets, and lettuce since we brought her home. Her nails are a normal length, but I haven't gotten a good look at her teeth yet. We don't know if she's spayed, but we're pretty sure she's a girl. For all we know she might be pregnant :| The only problem I can see right now is that she has oil (or something like that) on her back. How should I clean that off? I don't want her to ingest it, but of course I don't want to scare her either. Any advice would be much appreciated!

And now the moment you've been waiting for! Pictures! There's only two for right now because we're letting her settle in

She looks like a NZW! Sorry I have no suggestions about the oil, maybe google it - it might have some advice. Hope she settles in well.

The photos show a little yellow staining in places on her fur, which could be urine stains or from just living wild for a week. Can you show where the 'oil' is?
The safest thing may be to clip out the fur in the affected areas if it is oil eg from sitting under a car. It will get rid of it without the risk of it being ingested, although she may look tatty for a few weeks while the fur regrows. Otherwise, a slightly damp and soapy cloth or baby wipes may help - then wipe the soap out with just a damp cloth. Bathing a rabbit isn't normally recommended, will stress her out and may push any contaminant on the ends of her fur onto her skin - which may then be absorbed through the skin. A vet check may give you some more useful advice as well as a full health / teeth / pregnancy / gender check.

Well done for rescuing her.

She is absolutely stunning and looks like a cuddle rabbit.Thanks for rescuing her.
No idea about the oil though.

Shimmer the yellow staining is more brown in person and definitely feels like dirt not urine. We've had several rain storms this past week and she was outside during then so she probably got a little muddy. We will of course be taking her to the vet for a full check up. She is such a sweet rabbit and isn't scared of us at all.

Here is a picture of the 'oil'. It doesn't look as bad as it did yesterday.: