Are there any inorganic substances containing carboxyl groups?

Yes, there is. In fact, hydroxyl is not a patent of organic matter, it is just a substituent.

Water (H-OH), oxyacid (H2CO3 contains 2 hydroxyl groups, H2SO4 contains 2, HNO3 contains 1, HNO2 contains 1) or its acid salt, Na[Al(OH)4 contains 4], and calcium hydroxyphosphate [Ca10 (OH).