A girl is being sheltered in a temple by some monks.
She is treated like a V.I.P., she cannot go out...she's basically bored out of her mind.
So, to kill time she wants to wash the monks stuff. They say that she doesn't have to concern with those things and just rest her mind and body. She shouts that they don't have to give her a special treatment and she asks to let her do the laundry. She concludes with
てな = というの? like in てなわけで?
So is she saying "That's how I feel..."?
てな： という； というような； そういった； そのような
てなわけで＝という訳で； といった訳で； そういう訳で（generally pronounced そうゆう訳で）