The quality drops because placing a mine type building (including this one) reserves all of the mineral/oil deposit within a set distance. Deleting the mine restores the deposit to its previous condition.

You should be able to find the prospecting tool in the "List of vehicles and buildings" (see handbook icon on the left menu), in the buildings list under the filter: "Mines." Double click the entry to open it and then delete it as normal.

When I place any prospecting tool on the ground, quality drops to zero, and I can't remove tool and recover quality

Excellent work, comrade. The workers and farmers of my Socialist Republic salute you!