Are you using trcflg=0 or trcflg=3?
! --- 'trcflg' = tracer flags (one digit per tracer, most sig. replicated)
! --- 0: passive, 100% at surface
! --- 1: passive, psudo-silicate
! --- 2: passive, temperature
! --- 3: passive
How about trcrlx?
! --- trcrlx activate lateral boundary tracer climatological nudging
If trcflg=0 and trxrlx=T then the surface tracer is maintained at "climatology" everywhere that this isn't zero, and if rmutr is zero everywhere this is the only tracer forcing. If you want to continue the run but with exactly zero in the original subregion the closest you can get is to make the climatology very small but not zero (e.g. 1.e-6) there. If you instead want to continue but without any forcing, set trcflg=3.
If trcflg=3, set the climatology to zero and trcrlx=T and provide a rmutr that strongly relaxes to this value in the desired subregion. I would use 1/(4*batrop) for an e-folding time of 4 time steps. You could do this for just a day or two and then run without trcrlx from then on.