The only way to find out is to wash it, unfortunately.
This is because of the variation of the different types of inks from company to company and mainly has to do with whether it is a dye based ink or a pigment based ink. Because it has transfered, I suspect that it is probably a dye based ink - these ones when printed onto fabric without a mordant (ie bubblejet) will run when they get wet, whereas the pigment based ones are usually more secure onto the fabric.
By the way if you were to starch your fabric, the print would transfer to the starched surface rather than the fibres of the fabric, and probably be easier to remove - although I am sure that you would rather not have to remove them to start with