Per MSDS, it is decahydrate.
Okay. The box label on 20 Mule Team Borax doesn't give much information (though there is a link to the seller's web site for information and additional uses).
Washing (what the Gainer reference above is) is usually used to remove more soluble impurities from a less soluble desired product (at the cost of some loss of the desired species). For instance, if a synthesis produces, say, a yellowish impurity in your white target chemical, washing with a solvent that dissolves the impurity more readily than the "good stuff" will improve purity, but will lose some "good stuff" down the drain (or into the haz-waste stream). The larger the difference in solubility, the lower the losses.
Borax is fairly soluble in water, but given how most of it is produced (strip mining fossil dry lake beds, as I've understood it) it may still, after the manufacturer's purification to laundry grade, contain impurities of sodium carbonate, sodium bicarbonate, sodium chloride (and possibly other chloride salts), possibly phosphates of various types (I say that because those are mined the same way, though generally from different deposits) -- most of which are somewhat more soluble than borax. Most of us use borax in photography as an alkali that's not expected to directly take part in our intended reactions, however, and high purity isn't paramount in that application as long as certain impurities aren't present -- say, iron or copper salts if you're mixing Mytol (and those aren't likely to be much if any more soluble than borax anyway). A little boric acid does little or no harm (it'll lower pH a little, depending how much is present).
Unless Gainer wrote more to clarify what he was accomplishing with the water wash, I'd be inclined to believe it will do little to help, possibly nothing at all if you don't use water of high purity.