FIG. 1 is a front and right side perspective view of a door-mounted towel organizer showing my new design, the partial broken-line disclosure of a door being for illustrative purposes only and forming no part of the claimed design;

FIG. 2 is a top plan view thereof;

FIG. 3 is a front elevational view thereof;

FIG. 4 is a left side elevational view thereof;

FIG. 5 is a rear elevational view thereof; and,

FIG. 6 is a bottom plan view thereof.