I'd replace if possible. I have ziptied many even by adding new small holes. Most on the small vehicles like that are only held by the 2 piece plastic push clips that the center pulls out so you can remove it. Many of the older ones I deal with the spot where it goes into on the bumper cover etc rip out.
Was the road she was "supposed" to go down the same type of thing? When I was in college I used to take my '83 Civic Hatchback down roads like that. It was small enough that you could go around many of those rocks. They used to have parties / bonfires at the clearings after those areas. All the truck crowd were shocked when I showed up all the time.
Since she is 17 and probably pretty new at driving. I highly recommend you sign her up for a class at
WWW.STREETSURVIVAL.ORG it is a hands on class taken in your daughters vehicle with an instructor. Covers emergency lane changes, wet skid pad, emergency braking etc. The tires WILL get some edge wear but it will be a wealth of experience. My kids recommend it to their friends after taking it. The classes fill up quick.
If roads like that might be a frequent occurrence in her future, replace the ILX with a CRV, Forester, CX-5 etc.
Since you are in NH, I presume you have experience over the years with winter tires. For her it would be a solid safety investment to get 4 spare rims (smallest possible to clear calipers) and good winter tires. Rims should be easy on CL, FB Market, ebay etc. even from other brands with same bolt pattern, just watch the hub bore though Honda's CB is smaller than others. I use Hyundai rims on my Accord. I get 4-5 winters out of most of my winter tires. Rims last as long as I have it then get re-sold after.