Does Someone Have A Screw Loose?

I quite like the work of the Austrian artist Gustav Klimt [1862-1918] He was fascinated by Impressionism, Symbolism and Art Nouveau and created some spectacular works. He painted naturalistic figures- but often against sensuous, complex backgrounds - with rich colours, geometric designs and using deep and bright colours. On Tuesday, one of his paintings sold for a record sum.

Two of the most well known are "Portrait of Emily Floge" and "The Kiss" So I was quite excited to spot a jigsaw, reduced to £1 in the Cancer Research Charity Shop. It was in a round box, and the label informed me it was double sided, 19" in diameter, and had 500 pieces. I already have some puzzles yet to do, but this was a bargain!

It was from 'Past Times' - that retailer of retro goods which went into liquidation in 2012, and was bought out by WHSmith [I cannot call them TGJones] I have no idea how old this jigsaw is - but the plastic bag of pieces has never been opened. I suspect [like many PT products] it was given as a gift and never used. Emilie was a fashion designer, it is thought she designed - and maybe stitched - the gown. I know that Kaffe Fassett likes Klimt too, his knitwear is full of coloured patterns like this! 

Inside the box is the sealed bag, a small information leaflet about Klimt - and a small brass screw. We have no idea what it is - and suspect it has nothing to do with the puzzle. But how did it get there? and what is it for? 
Perhaps someone was clearing up the Christmas decorations and found it on the floor, so popped it in the box, and forgot about it.

Which side should I complete first? the blue Emilie, or the golden Kiss?