I tried removing all mods and the issue is still there. However, if I start a new game and drop ursine gear via console, it's not present. Does that mean my save file has traces left?
Yes. Reference data for mods that get saved in the save-state will remain forever more. If the mod is removed, and the data referenced no longer exist, the references themselves may leave holes that the game no longer knows how to deal with. Might do absolutely nothing, might create small issues, might make the game unplayable. All up to how the mod works and the state of that playthrough at that point.
The only real solutions to this are to re-install exactly the same mod setup that you were using previously, then reload to a save that was made before any issues first appeared...or re-install the game (to be extra safe) and begin a brand new playthrough.
Is there anyway to open the save file to see if a trace is left there?
Technically...yes. But it would require to you have precise knowledge of how both the mod and the game created the reference data, then go back and manipulate the data (probably using a hex editor). This would require isolating every single aspect of the data affected by the mod (potentially hundreds), and that still does not mean that the resulting changes would be recognizable by game, as those results may not reflect the correct progression of the game vanilla conditions. It's probably worth a look, if you know how to do it (...I personally have no idea...), but it's likely not worth the effort involved.