Curios: 2.0.2.1.
Forge: 31.1.36

When Curios is open other mod's inventory additions like buttons or slots are removed. It would be neat if that wouldn't happen.

I'm not sure if this is really feasible to fix, but I have an idea I'd like to try first. In order to duplicate this issue properly, I'll need to know which mods are adding those particular buttons in your instance.

Extreme sound muffler (Forge) adds the sound box at the top center.
Quark adds the square button on the right center.
Quickstack adds the 2 larger buttons next to the button of Quark.
TrashSlot adds the trash can slot.

Unfortunately my idea didn't really pan out and I don't think there's any good way to fix this on my end. The mods that add those extra features would have to do the same thing to the Curios GUI that they do to the vanilla inventory GUI.