The control valve's Brine Port, should be open while drawing in Brine (O3) during the Brine Draw cycle.
For a water softener, water will exit the Brine port during the Brine Fill cycle to refill the brine tank, but since your unit is configured as an O3 filter, an actual check valve installed externally on that port should ensure water does not exit through the brine port during Brine Fill, if programmed, but will allow O3 entry during Brine Draw.
The check valve is not a 'button', but your reference to a button leads me to suspect you are referring to the BLFC (brine line flow control) flow restrictor, which is a button (washer) that utilizes a small tapered hole to restrict the flow rate of water that exits through the brine port to the brine tank.
While your control valve may benefit from rebuilding, if water is only exiting during the Brine Fill cycle, perhaps the issue is simply a defective external check valve on the brine port? During the Brine Fill cycle, filtering to house fixtures will be active.
The other check valve needed for an AIO or O3 filter, is within the supply line directly before the unit's inlet connection. As the air or O3 gas accumulates at the top of the filter tank where the unfiltered water enters the tank, a check valve is required to prevent the pressurized gas from leaking out backward into the supply line. This is particularly important when there is any upstream pressure loss such as that resulting from the system pressure dropping by ~20 psi to cause the pressure switch to activate the well pump.
