Wow, I read through most of what was said here, I can't believe you got a finished product that looked like that from a shop, they should be ashamed of themselves.
I would take it back and ask for some sort of refund. If you decide to work around it by stippling I'd ask for half my money back, if you decide to remove it and applique on a new banner, I would ask for all my money back.
I wouldn't take the stitching out, it's a bear to remove stitches and it does break down the fabric and if you aren't careful, you could also create holes or tears in the fabric.
I think stippling around it is the best suggestion, although you will really have to be careful that you are not reinforcing the puckers or creating small pleats, it would be tricky but it can be done.