I claim the ornamental design for the burger press tray, as shown and described.
FIG. 1 is a perspective view of the burger press tray, showing my new design;
FIG. 2 is a top view of the burger press tray;
FIG. 3 is a front view of the burger press tray, the back view being a mirror image;
FIG. 4 is a left side view of the burger press tray, the right side view being identical;
FIG. 5 is a bottom view of the burger press tray; and,
FIG. 6 is a perspective exploded view of the burger press tray, including a plunger and lifter shown in phantom which form no part of the claimed design.