A process for manufacturing a cellulosic paper product (e.g., paper hand towels) exhibiting reduced malodor upon wetting. The process comprises forming an aqueous suspension of papermaking fibers, depositing the aqueous suspension onto a sheet-forming fabric to form a wet web, drying the web at high temperature in an oxidative environment and topically applying a liquid glycol composition comprising a glycol compound selected from the group consisting of polyethylene glycol, triethylene glycol, glycerol and mixtures thereof to the web having a dry weight consistency of at least about 80%. The process of the present invention is particularly suited for reducing malodor released from cellulosic paper products made from through-air dried base sheet material.