3'-5' RNA exonuclease that trims the 3' end of oligo(U) tracts of the pre-U6 small nuclear RNA (snRNA) molecule, leading to the formation of a U6 snRNA 3' end-terminated with a 2',3'-cyclic phosphate (By similarity). Participates in the U6 snRNA 3' end processing that prevents U6 snRNA degradation (By similarity). Belongs to the 2H phosphoesterase superfamily. USB1 family.