Does copyright law allow you to restrict use of your observations—the data, this is, not the photos?

I googled GBIF’s terms which explain some of their rationale for licensing choices. They also go into a bit of their thoughts behind non-commercial uses and basically say “there’s a lot of grey area, but GBIF isn’t in the enforcement business.”

I believe that the GBIF/iNat downloads also include a field for the licenses that each observation is licensed under, so you would need to include that in your supplementary file as well. Technically, you should provide a link to the licenses that apply to any observations that you used, though to my mind this is less important as anyone can google the licenses as long as you provide accurate info about which they are.

In terms of changes, I am not an expert in this, but, based on what I’ve read, a paper will describe how the data has been used, and you aren’t really “changing” the data so you should be ok there. The export file will have the original data, so you wouldn’t be distributing modified material, but the original data I think. I think this requirement applies more to situations like photoshopping images, etc. Technically you would also be distributing the dataset from GBIF which is licensed as CC-BY I think (again, see their terms).

Depending on your usage and the licenses, you might have an issue if you were to publish something for profit or with a more restrictive copyright license. See some discussion on use of images here:
https://forum.inaturalist.org/t/surprised-to-find-photos-i-placed-on-inat-in-the-new-audubon-mushroom-guide/40986