Include a mistake that cost extra when asking for reimbursement after faculty interview?
Assuming they liked your presentation, and consider putting you on the shortlist, but are not sure at which position compared to some other candidate; now, reflect, which impression this makes. 


You made a nontrivial mistake which is also quite costly.
You ask them to cover that mistake of yours.


Even if they would be willing to do so (and assume it would be eligible at all, which is also not clear - why should they reimburse you for your mistake?), consider how this comes across.

Unless you really are in dire need of the money (and it's not clear you are going to get it anyway), it's probably the wise thing to let things be.