Responses

American here! A sloppy joe is generally a mixture of chili and ground beef sandwiched between two hamburger buns. So the joke is that the girl possibly *didn't actually* write "I love you" with the sloppy joe, but that the girl rather just slapped the Very Messy food item onto the desk, and Haru just saw the chili-beef mixture and "saw" the phrase in the messy slop.
The translations is very "americanized", had to search what a sloppy joe is.