Sadly it was fitted by a bodger who doesn't know how to putty in glass.
The paint is chipped and it will be easier to smooth and paint it without the glass.
If you are handy, you could take it out and do it again properly.
there is a modest skilll to using a putty knife, I can do it, but I'd suggest you scrape off all the putty, sand the wooden rebate smooth and paint it, fit glazing tape (this is a plastic foam tape, thick enough to absorb slight irregularities, sticky on both sides, very very strong adhesive which will defeat burglars), fit the glass and retain it with quarter-round or square wooden beading on the inside only, painted to match the inside face of the door, and retaine with small brads or very small brass or stainless screws (the special tape will actually hold the glass securely, the beading in that case is just for appearance).
Or you could reglaze it using glazing compound, which is a sort of modern selant, I think it is acrylic based.
An older builder or carpenter would know how do do it properly. Putty is no longer in common use.
