NEW YORK — Bill Murray has walked onto David Letterman’s show dressed as Liberace, a jockey and a football player, flown onto the set in a Peter Pan outfit, worked out while singing “Let’s Get Physical” and dove into a water-filled dumpster strewn with garbage. This week he’ll be saying goodbye. Murray’s 44th and final appearance Tuesday will mark the end of late-night television’s most unique and enduring host-guest relationship, with years of oddball humor by two comics whose sensibilities seemed perfectly aligned. Letterman ends his 33-year run as a late-night host the next night. Murray, the former “Saturday Night Live” player turned movie star, guested on Letterman’s first “Late Night” on Feb.