Modifying the EXIF is one way to get around this. Of course the system depends on the honesty of the people entering photos if they are editing EXIF data.
If you can't edit the EXIF, another option is to delete the EXIF data completely (if you can't do that easily, convert it to PNG, and then convert back again - PNG doesn't do EXIF).
Then enter it into the competition.
You'll then get a warning that the date of the photo can't be determined and the entry is only a tentative entry. It will display a link to click on in order to email your proof of date to the competition admin. Click the link and send some sort of proof of date taken. Not sure of the current status, but when I was the competition admin, it didn't take much to convince me.

The admin can then log into the system and enter the actual date taken into the system which will complete the entry into the system.