rear hatch

Yikes! I think you've got close to 0% chance of warranty coverage. Unfortunately, it's a painted part which adds to the expense of replacement. You might get lucky and find one at a junkyard in matching paint.

I'm not sure what to call it either, hatch handle?

 

That part is called "Back Door Garnish Subassy Outside". Please do not think of it as a handle, since that thinking is what caused the OP's current problem.

You can buy a painted replacement for $117 here:
2007 Toyota Prius Parts - AutoNation Toyota Gulf Freeway Parts

Note the price increases to $151 since you have the Smart system.

 

Seems reasonable to call it a handle since that's the only thing available to lift the hatch (except the spoiler which is clearly not a handle). I'd agree, too much force was applied, however it's clearly a "handle" to me.

I'd bet either the latch didn't release or the hatch was frozen closed.

Nice that you can buy a painted part, unfortunate that you can't simply buy the housing but have to buy the assy with the release & SKS components.

 

During very cold ambient temps when the hydraulic "back door stays" are not exerting much force, the hatch will be relatively difficult to move upwards.

I suggest that the hatch be lifted up just a couple of inches; then place your hand at the bottom of the hatch sheet metal, to continue the hatch opening process. That will preserve the back door garnish subassembly for its cosmetic purpose.

 

Based on that picture, it looks like it wouldn't open at all. I suspect it was frozen closed - I've had a door freeze closed that required significant force to open (fortunately, I had an actual handle to pull on).

 

When that happen to me I get inside thru any door that will easily open and then push the others open from the inside. Ice can make it impossible to get in some doors and you can easily break handles off. Even then it is still possible to pop off some rubber door gaskets, but usually they can be fitted back on...

 

Ebay sells this item too. I've been looking for one of these as the Prius I just bought has a broken garnish. It looks as though it's just clips that broke, I might try some strong glue and glue the plastic clips back.