As I mentioned yesterday, this issue was addressed during the press conference. They stressed that the minimum detection sensitivity of their exposures was sufficiently below the level of the faintest white dwarf detected to rule out the likelyhood of there BEING fainter white dwarfs that they DIDN'T see.
But you are correct in noting that they intend to do further imaging, using the vastly more sensitive camera just installed last month on Hubble, to verify (or refute) their initial findings. And they DO intend to use more distant clusters than the one (M4) used in the current study.