You will need to get that lasered and then covered.
The above tattoo is a very well done tattoo while yours looks like it was done by the first available tattooist. A refund is highly unlikely unless the tattooist misrepresented himself. Did you look at their portfolio? was there anything in their portfolio that lead you to believe that they could pull off this tattoo?

I would go to a few well known, highly rated tattoo artists and ask them about it. It may be able to be refined or covered without being removed by laser. I have a small tat of the nickname “Babe” on my chest. I had it done by an artist who was less experienced than I knew. After it healed it looked all jagged and just plain ugly. I went back and showed it to the shop owner, who by that time had fired the artist, and he redid it and refined it and it turned out great. Best of all, he did not charge me for the redo. It really depends on how experienced the artist is who fixes it. Getting a few different professional opinions first is best.