How to form biological metallic tissue?
First and foremost, it looks like the original article is slightly less dramatic:


  Parasitoid ovipositor tips have a higher content of the transition metal zinc compared with the cuticle elsewhere on the ovipositor


So a 'higher concentration' isn't quite the same as 'tipped with'. It looks like they are describing a higher numbers of metal ions, rather than pure metal:


  The presence of transition metals in insect cuticle and mandible is hypothesized to increase material hardness to permit cutting through hard substrates with minimal wear 


There are many examples of organisms using inorganic chemistry to make materials. The overall topic is called biomineralization and you even mention teeth - which is hydroxyapatite (not really organic chemistry!).

However, a pure metal like zinc is unusual, I think. There are examples such as the snail that has an iron pyrite 'armor' or even the iron nanocrystals in ferritin.

More spectacular examples include the bacteria that produce gold particles


  As a result, Au
  detoxification is mediated by a combination of efflux, reduction, and
  possibly methylation of Au-complexes, leading to the formation of
  Au(I)-C-compounds and nanoparticulate Au0.


Where Au0 is pure gold. I don't know of any other examples of pure zinc in organisms, but there is a nice review here of zinc biochemistry.

When you say 'synthesise' I assume that you mean 'deposit'.