To remove the blue marks - there is a toy item available at wall mart called an aqua doodle. 2 refillable pens for about $4.80. Get them and fill them with a mixture of 1 Cup distilled water and add 1 tsp of baking soda. I put this mix in an empty water bottle and labeled it. I doesn't spoil and you won't need much. Now just go over the lines and they are gone. This doesn't push the blue into the batting. I've tested this procedure for the machine quilters group and it works! If you are desperate and don't want to go get the pens give a q-tip a try. This way you don't have to soak the quilt.
Happy Quilting - Sally