Have a look at your AWS billing console, since data egress is charged and downloading to verify is considered egress.

AWS S3 supports data checksums where a checksum is calculated at AWS, which you can compare against a checksum that you calculate locally.

This is an article that goes into how it works, but I've not (yet) tested it, but I'll be following in your footsteps pretty soon.

https://medium.com/@maureenosaghae86/check-the-integrity-of-data-in-amazon-s3-with-additional-checksums-3e51fe45f530

As an aside, make sure that versioning is OFF on your backup bucket unless you specifically require and understand it, because even when you delete objects, they persist as a previous, all but invisible, and charged(!), version.

My former backup software "helpfully" enabled versioning and I was left with a $600 monthly bill for six months while there was no actual backup being done due to a local hardware failure, until I figured out what was happening. I used that software for years and shudder to think just how much extra it actually cost.

I will note that while I had a catastrophic hardware failure, I didn't lose any data.

Finally, if you're storing data in Glacier, retrieval is charged at different rates, depending on timelines of access, so it might be that your backup software is using the slow tier to "save" you money.

Edit: OP advises that they're not using AWS, instead they're using OVH. The object storage solutions appear to be mostly compatible, but I was unable to discover if the OVH implementation supports checksums.