How Good Are the Upper Limits on Heavy Elements?
Good question! Normally, the lack of heavy elements is taken as an indicator that something was made from (close-to-primordial) gas.

So an answer could be to ask what are the lowest abundances ever measured with respect to hydrogen.

I am not completely up to date with the current record holders, but stars with iron abundances that are 5 orders of magnitude less than in the Sun have been found (Norris et al 2013). This corresponds to A(Fe)$\sim 2$ on the usual logarithmic scale where hydrogen has A(H)=12.

The constraints on other iron-peak elements are similar. Alpha elements like O, Mg are usually enhanced in very metal poor stars, so the constraints are an order of magnitude higher.