I use Goo Gone to remove the sticky remains of size stickers on clothes. It is citrus-based and quite strong, but if you wash it right away it should not hurt polyester. It is available in many stores, but Home Depot has a larger-size spray bottle at a good price. Target, craft stores and other stores that sell laundry products often have it. It works best when you put it on and let it sit, so it can dissolve the adhesive. Look for a bottle with an orange label and top. Works great on price stickers on all items.

I have a can of cigarette lighter fluid that I use to remove any and all stickiness from all sorts of things. Also does a great job of removing ink.

I actually learned of this years ago at a store when buying something and the clerk removed the sticky tag for me with this.... lifted it right off and wiped off the spot with no signs it had been there!

It does have a bit of a smell and oily feel, but it washes off easily.

Much cheaper than goo gone, and personally I think it works better/easier/quicker.

ymmv!

Please be careful with lighter fluid. It is very flammable (obviously) but it can also dissolve some of the new fabrics and finishes on items these days. It can dissolve carpet fibers and mar wood and plastic surfaces. Be sure and store it far away from children or pets. Most of the cans have a little spout that is difficult to open and close so people tend to leave it open and it spills (or worse).