So! It's a crumbled paper ball, based on the design of "the culprit"* from Detective Conan. But this is just a suspect, so one will have to observe their behavior and use acts to see if they're innocent or guilty of a "crime". Then you can spare them! Here are the designs for the innocent and guilty forms.
*For those who don't know, its a design to show details of how the crime was committed, but not to reveal which of the suspects committed the crime. Danganronpa also does a similar thing in the case summary part of trials.
For their Light World objects, the innocent Suspeculiar is a receipt for something Asgore likes and wanted to buy, like a new watering can or special fertilizer. Their paper ball is super light, since it's not weighed down by guilt. And since it's "morally good" it also has a flower motif, since Asgore likes flowers.
But the guilty Suspeculiar is payed bill or taxes in the Light World. Guilty Suspeculiar are reluctant thieves, they feel remorse for "stealing Asgore and Carol's money" but they must do it. This reflects Asgore's view on bills, they're hurting his situation and he hates paying them, but he knows he must and they're probably financing the larger infrastructure to provide electricity, water and stuff. Their paper ball is heavy, and they roll it like Sisyphus/dung beetle. They also have a bit of an aphid motif, since those hurt flowers. Oh yes!! also their hands are cuz "they're caught red handed".
(Pun name explanation: Suspect + peculiar + liar)