FIG. 1 is an exploded front elevation view of the trap for flying insect pests showing the new design; FIG. 2 is an exploded rear elevation view thereof, opposite the side shown in FIG. 1; FIG. 3 is an exploded side elevation view thereof, with the opposite side being identical; FIG. 4 is an exploded top plan view thereof; FIG. 5 is an exploded bottom plan view thereof; FIG. 6 is an exploded isometric view thereof; and, FIG. 7 is a sectional view shown along line 7-7 of FIG. 4.