grab-site doesn't rewrite URLs, it captures the entire request and response of each http request for an asset and stores as-is for archival purposes. The quality of any mutations or transformations performed will be governed by the tooling used to consume the generated WARCs.

More detail on the WARC format can be found below:

https://www.loc.gov/preservation/digital/formats/fdd/fdd0002...

https://en.wikipedia.org/wiki/Web_ARChive

http://fileformats.archiveteam.org/wiki/WARC