The ornamental design for a foodboxcoveringdevice, as shown and described.
FIG. 1 is a perspective back view of a food box covering device showing my new design;
FIG. 2 is a perspective front view thereof;
FIG. 3 is a bottom view thereof;
FIG. 4 is a side view (opposite side view is mirror image) thereof;
FIG. 5 is a top view thereof;
FIG. 6 is a cross-sectional view of FIG. 1 thereof; and,
FIG. 7 is another perspective back view in a condition of use.
In FIG. 7, the broken lines showing of environmental structure for purposes of illustrating the food box covering device in a condition of use. The broken lines and the structure they depict form no part of the claimed design.