Vinyl advertising tarps are composed of a mesh of polyester fibers sandwiched between two layers of vinyl. The mesh gives the tarp its strength.
Sometimes after cutting in the Cricut Expressions the cut edges will have quite a lot of protruding fibers. Individual tarps have more or less of this fiber after cutting. I was thinking that my lace experiment was not going to work until I thought of this way of dealing with the fibers.
I found that if you pass the material over a candle flame that the polyester fibers shrink and recede. Timing is important. Too much and the material will smoke and burn. Maybe about a half of a second, more or less, is ideal. It is not a perfect solution but I was able to clean up my lace significantly. Note: the slight melting induced by the candle does not cause toxic fumes as you are just rearranging the polyester molecules and not putting them into the air; heating until it smokes however, does. If you are concerned about fumes, make sure you are in a well-ventilated area.