Ptkay, are you sure that is a Honeywell FMS? Honeywell typically prints their name in the upper left of the bezel. Collins and Universal put their names centered on the top of the bezel. The display above the FMS is a Universal MFD-640, and it's been reported above (by USA Today) that the TAWS was a Universal TAWS, not Honeywell. I'm guessing the FMS is Universal as well.
Smolensk UUBS is not in the Universal TAWS database (not in Honeywell EGPWS either) according to their websites, so the TAWS would give nuisance alerts during every approach/landing unless those predictive functions were inhibited by pilot. If they were inhibited, all they're left with is the rad-alt based GPWS modes, and as stated earlier without ILS and in a stable descent there would be no alerts, except the routine altitude calls if enabled.