Bird in love with my mirror glass windows

Hi,
I have replaced my windows with ones with a mirror finish.
Now one particular bird, I believe it is a Bluetit, has fallen in love with his/her own reflection and visits one or more of my windows every morning and randomly thru the day, creating a noise like a tiny jack hammer. It is not after the joints in the window frame (PVC) or insects; it just keeps pecking the glass, as in it's own image. I even have video of the little 'darling'.
I would appreciate any help as shooting may damage the glass.