I don't know what it is, but it seems to appear on jars of olives too.
I don't like it and am a bit wary of it, so I rinse any pickles or olives and pat them dry on a clean paper towel and then redo them with fresh vinegar or strong brine. Then I keep them really cold and eat them up pdq.
However, having looked around the net, apparantly it's really common, and the advice from chefs is just to spoon it off and top up with fresh vinegar....the stronger the better.
Others suggest loads of chemicals and some make comments about keeping the jar scrupulously uncontaminated with fingers or cutlery that hasn't been freshly washed.
I don't fancy the chemicals and my cutlery is clean, and some of my brined olive jars ended up with the same greyish scum.
Up to yourself; I know I'm a fussy besom, and Mike 313's comments make sense to me when even my nothingbutcleancutleryinthejar ones go cloudy too. Opening up the jar and letting air in seems to be enough.
I agree with BR that good vinegar keeps for a long time, and good chutneys seem to be fine for years (I opened a jar that was eight years old and it was delicious
) but I think a lot of modern vinegars aren't strong enough and they have built in obsolescence so that like Tam folks chuck them out after a couple of months while old style vinegar jars (like rumtopfs) were used for years.
Unless there's even the slightest whiff of sh1t when you open up the jar, it's probably safe to eat the contents though, regardless of how unappealing the grey scum looks.
M