Freeze-thaw damage happens at the moving ice front, not at the storage temperature. Once the sample is frozen solid and cold, very little is happening. The damage is done during freezing and thawing, which is why the number of cycles matters and the duration of the hold mostly does not.
On re-freezing something that thawed in transit: if it arrived as a lyophilised solid that warmed but never got wet, re-freezing costs you nothing except the thermal cycle. If it arrived as a solution that thawed, re-freezing adds a second transition and therefore a second dose of ice-front shear. The asymmetry is worth internalising.
Specifically, for the solid state, residual moisture is the dominant variable. A cake at two per cent water is considerably more stable than the same cake at six per cent, because water is both a reactant in hydrolysis and a plasticiser that lowers the glass transition temperature. This is why a desiccant in the outer packaging is not theatre, and why opening a cold vial in a humid room is a genuine error — you condense water onto the cake.
The practical rule is that time and temperature multiply, so shorten whichever one you control.