Since you said it doesn't have anything to do with the theme, it probably wouldn't fit anyways. Quoting the Ludem Dare rules on using the theme:
To us, the Theme is just a single voting category. Ludum Dare is about encouraging you to make something. The theme is something we do to help everyone with the “blank sheet of paper” problem that artists and creators deal with. It’s easier to make something with some direction than none.
That said, it’s worth understanding that all voting categories in Ludum Dare are opinions; The opinions of your peers. So while we don’t enforce that your game meets some minimum “themeyness”, the community does see significance in the Theme. So while we wont do anything about it, the community as a whole prefers games that do use the Theme. So as a general suggestion, if you want to score well in Ludum Dare, make sure you do use the theme in some way.
Using the Theme in Ludum Dare is a Social Rule, not a Legal Rule.
It is fine to prefer games that do use the Theme, but don’t be a rude about. A game made in a weekend doesn’t always turn out the way you hope.
While I understand this isn't a Ludem Dare (and thus you might be required to use the theme), I'd say that their statement accurately sums up most, if not all, jams that utilize a theme; including this one.
That said, there are many other places that you can show off your work.