In the case where you had three tasks under one story, and only completed one task (not the entire story), your Burndown report should be able to show that you still had work items open at the end of the iteration. You could use this to interpret technical debt if the work items are not updated/moved to another plan.

In regards towards your question for the best procedure, this is tough. I would suggest whatever you do decide, make sure it is documented as a standard and used in all cases moving forward.
Since the first task was completed, and the others become the 'technical debt', you could move them onto the backlog. Otherwise if you bounce them around between different iterations they may never get completed, or may cause additional technical debt in other areas if your team pushes to complete them (and neglects other features). At least when they are in the backlog, you can re-evaluate them during your sprint planning.