Filter recognition from transfer function
From one of your comments it appears that you've actually already answered the question. Here are a few remarks and questions that should help you gain some more understanding:

If you have a transfer function $H(z)$ (and if you assume that the corresponding system is stable), then the frequency response is obtained by choosing $z=e^{j\omega}$.
For $H(z)=z^{-k}$ figure out the magnitude and the phase of $H(e^{j\omega})$.
If the magnitude of $H(e^{j\omega})$ does not depend on frequency, what kind of filter have you got?
What is the input-output relation of the given system?