How can I fix these scratches on the rear bumper ?

Based on the pic, doesn't look like a DIY job, particularly since the upper part of the bumper is indented.

Having said that, for the part below the horizontal crease line, rubbing compound, polish and wax might make it pretty much unnoticeable to most casual observers. Above the horizontal crease line, a bottle of touch up paint, applied on the black spots, in multiple--very thin--coats, might also hide the damage well.

But if you're looking to get it back to factory new, you're looking at a professional job, and most likely replacement of the bumper, since attempting to repair the indentation on a bumper isn't a good idea.

 

If you know how to paint, you can buy a new bumper cover and paint it, then install it. Else, buy a new bumper cover, pay a body repair shop to paint it and install it, or just have the body shop do everything. Probably about $800 - $1000.

 

I have a similar issue with our Lexus. I've searched far and wide, so here's my opine.

1. Touch up - too large an area - no way would it look OK - but if OK is OK, then you can touch it and wipe lightly. It won't look good.

2. Body shop - sand and paint will be $500+ - any way you look at it (two stage paint) - even at some random $99 paint shop. The whole thing must be primed and worked.

3. Find one used. This is a funny strange proposition - being on my second Prius III, I've done some searching, and bumpers show up on Ebay. All silver colors are the same. So if you find a better one, you could buy it, and put it on yourself. I've put links to me taking off the thing to put on parking sensors - job takes a mechanically sound person 1-2 hours tops to pull off the current cover and swap it.....
I saw one for like $150 delivered in great shape...

Your best bet is finding a good one, swapping it. Second best is buying the touch-up (F7J paint?) - and filling the scratches. Use paint thinner to wipe the surface clean before and after...
EDIT: Here's everything you may want to know about the bumper removal process.

http://priuschat.com/forums/gen-iii...tions/69601-very-cool-parking-assist-mod.html - you could also just pull the thing off, and take it to a paint shop - you'd likely get a great deal at some spots - or maybe they could patch it for a few $$$

Someone clipped my front corner - took it to a real local shop, and they fixed it for $50...

 

I think you should make a claim to your insurance because it will be expensive to repair the bumper and the cracked tail light.

 

I feel your pain. I parked my car at a restaurant and when I came out I found a huge dent/scratch on the right rear bumper. Estimate from the deal came back at $765 to replace the bumper and $739 to repair the bumper. I went to another dealer and the estimate was $520 to repair the bumper. I wish I caught the person who hit my car! The first dent is always the most painful.

 

Being a cabbie I'm an expert of buffing out scratches - and I can tell you that scratch isn't going to just buff out. It'll need a professional job that's for sure, esp as the back light is broken. Don't know how the law stands in the US but a cracked back light would be illegal over here.

Whether you'd want to claim on your insurance is entirely upto you and depends on your claim history and excess/deductable. I personally wouldn't claim for it and would use a cheap, but reliable bodyshop for the repair and pay it myself.

Perhaps this would also be a good time to install a set of reversing sensors?