At this time Toodledo does not support the syncing of checklists.  This is a limit of Toodledo, not Informant.

When a task with a checklist is synced from Informant to Toodledo the checklist items are converted by Toodledo to standalone tasks.  These tasks as you see them in Toodledo are then synced back to Informant as new tasks.

To avoid this you will want to make sure that your tasks with checklists are not assigned to your Toodledo sync account and are assigned to informant sync instead. To do this, edit your checklist and go to the 'project' option. Tap the project name shown and choose a project under the informant sync header.