Tc⁷⁺ is very strongly acidic and will exist as an oxo anion in the form TcO₄^-

Recall for MO_x^y-:
pK_b1 = 10.0 + 5.7x - 10.2y
pK_b1 = 10.0 + 5.7(4) - 10.2(1)
pK_b1 = 22.6  =>  this is non basic and will persist in water

Alternately: formula evaluation yields "TcO₂" which is non basic.

Feebly basic anions would also persist in solution; moderately basic anions would be partially protonated; very strongly basic oxo anions will probably be protonated beyond the hydroxo anion stage often forming an insoluble hydroxide or oxide.