A few years ago, I found these plastic storage caps. While they can't be used to actually "can" the jam, they are fantastic to use on opened jars of jam or to use when storing leftovers in the mason jar. (The standard metal lid and screw on cap are great, but when replacing sticky jam or jelly each day, they become a nuisance. The metal lid should not be reused and I prefer the plastic lids for everyday use. They are easy to clean.)
I went to the hardware store and picked up some grommets. They are little and rubber and cost 55 cents each. I measured the hole I needed for the diameter of the straw and found that I wanted it to be just smaller than a centimeter. When choosing your grommet, measure the ID (inner diameter) and make sure that is just slightly larger than the straw you want to insert. There should be some room around the straw, it should not be snug. After you find your grommet, choose a drill bit that is just slightly larger than the ID of the grommet.
Insert the grommet into the lid, so that part of the grommet is on the top of the lid and part is on the bottom.
Insert your straw and there you go! The grommet keeps the straw from pushing out and moving around. It also makes the to-go cup look a bit more finished.
But, it is not necessary. Here is one lid that I drilled without the grommet.