Is it all green but with the same shape leaves?
Is it coming from the graft point? Do you have a photograph.?
I used to work in a garden centre, and saw this problem there. The pretty variegated top bit is always grafted onto a different rootstock - some sort of plain, ordinary willow I think - to give it stability. Use secateurs to remove the rogue shoots as close to the stem as possible, and be vigilant - you might find they grow again.
I find that pulling sharply down on the green shoots removes the growing point and helps prevent regrowth.
I don't doubt that's true Verdun
Great stuff you two - would love to see you both in action! Only prob with pulling shoots off is if they're too big & beefy, when they damage the tree stem. Otherwise, great advice!