Grip the edge of the tape with your finger tips and peel it off the linoleum. If the tape hasn't been on the linoleum very long, this method usually removes the tape in tact. If the tape tears and peeling doesn't work, go to Step 2.
Smear a thin layer of petroleum jelly over the tape with your finger and let it set for 24 hours. The petroleum jelly will soften the tape paper and adhesive during this time. Scrape the tape off with a plastic putty knife. The plastic ensures the blade won't do any damage to the linoleum. If any adhesive residue remains, go to Step 3.
Apply rubbing alcohol to a soft sponge and scrub off the remaining residue. Wash the linoleum with soap and water using a washcloth. Dry the floor with paper towels.