Why does the F-15 have a swept-back trailing edge at its wing tips?
The F-15 wingtip is a "raked" tip configuration, which increases lift and decreases drag.1
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This is the design decided by the USAF after discovery of several design deficiencies during initial flight test which included aeroelastic deficiencies (wing bending) and aerodynamic effects (buffeting). "In early June 1974, the Air Force flew the “raked” tip configuration and were completely satisfied
with the configuration’s buffet characteristics."  The Saga of the F-15 Wingtip