You'll not be rewinding that transformer. The assembly is 6 mm (1/4") on a side, and it is "not user serviceable", in that the winding is probably bonded to the core, the core is bonded into the tiny plastic package, etc. And then, you don't know how many turns on each side. or the wire gauge (other than "very small" - it's probably AWG40 or smaller)
I'd just buy a transformer with what you need. Or use it at 1.5:1 - if you're hooking it up to a VNA, it doesn't really matter, because you would be calibrating out the turns ratio in any case.
or buy some cores in a more practical size and wind your own. You'll need to make sure you get the right mix, and deal with the whole wire size, number of turns, how to put the windings on so the capacitance is well controlled. You'd have a tough time beating the <$4 each that MiniCircuits wants for something like an ADT1-6T.
Farnell (in UK), Newark, Digikey, Mouser all carry various mfrs of transformers - Murata, Johansen, Coilcraft, and Minicircuits are probably the most likely.
