I haven't read all the answers, but I will give you my answer anyway.
This kind of things happen from time to time. Either they didn't use a stabilizer, or didn't hoop it correctly. If you rip it it will show the holes.
I would turn it backwards and press from the back using the heaviest starch you can get, like a professional one or starch made for jeans. Press hard with the iron as hot as the fabric and thread allows you. You may be able to smooth some of the puckers. If this doesn't take care of everything, as said, do micro stippling between the letters. Use the smallest thread and the smallest needle you can handle. I would use a 65 needle with 60 wt thread, maybe Bottom Line. Use the same color on the top and bottom. Please show us what happens.