For the op-amp LT1490 in your text
You won't damage the op-amp by exceeding the supply at the inputs, so probably there is just a small current flowing. You should be able to just drive the DAC outputs low. If there is still a tiny current it might just be leakage through the p-channel MOSFET, though that should be very small (nA). If that is bothering you, drive the DAC outputs low and use a high value resistor across the power supply (maybe 20% of the Iq of the op-amp).
Edit: Because the 10V maximum gate voltage of the load switch (mentioned in the text, not the schematic) is being exceeded it's possible that Q5 is heating (due to the internal zener diode used on some MOSFETs to protect the gate) when on, and thus has much higher than normal leakage after being turned off.
Below applies to the op-amp in your Schematic
You are exceeding the absolute maximum ratings- which state that input voltage cannot exceed the supply voltage rail at all. Your feedback resistors are reasonably high value, so differential voltage is probably not a problem but you may have damaged the input transistors by exceeding the supply voltage at the inputs. Adding a BAT54C dual small signal Schottky to the inputs might be a good idea.