How soon can you fix a badly done tattoo?

Hi! I got my tattoo done last monday so a week ago. It was done with grey ink and i guess it doesn't stay well in my skin. At least thats what the tattoo artist that did it said. In my opinion he did the linework and shadowing very unevenly. He offers me a time in three weeks, where he would fix his mistakes. He has done other tattoos on me that look fantastic, but this one has a bit more different style. I also contacted another artist who has done tattoos on me in a similar style that i am pleased with. She said that I could gey it fixed by tomorrow. How quickly can i get it redone? She said that it's fine as long as it is not red or tender... The tattoo is causing me a lot of anxiety.