I would cut out the green and and sew another green in place of that then cut the lettering out and sew it on.. but before that I would get my money back and some for the whole item and time you put into it to replace it , this would let them know what they did wrong, also if they were a pro at that work they would have stabilize the area so it would not do that puckering..
good luck and I am so sorry that happened
KandiKane