I don't understand.
You PAID the shop to do the embroiderey and they screwed it up and you are not going to let them know?
Now you are going to try and do some more stitching around it to flatten it?
What if when you do that you are still not happy with it?
Please, go back to the shop, show them the problem, tell them it is not acceptable, ask what can be done to make it right.
By not doing anything and trying to correct it yourself, you are not helping the next person who goes in and gets some embroidery done. The shop needs to know so they can correct it and if they cannot correct it, they need to refund your money.