How can I repair damage caused by turtle wax scratch repair kit?

Okay, well first of all. The degree of the scratch will determine whether or not a buffing compound will work or not. You can't just buff out a scratch that went through the clear coat. No one can, period. Hopefully you used a fresh pad and rotary buffer in the first place. Using anything else is just not smart nor efficient. Compounds that "fix" scratches are only successful when used on the clear coat. Most or all compounds will not fix anything that is any deeper than that so in your case, you should have never attempted this in the first place. Not to mention, claying the car before hand is essential for results. The pattern you use the rotary buffer and the type of pad you use is almost crucial. Sorry but taking it to a shop or painting over it is your best bet. Online chip kits are scams and none of them work, ones that help are only temporary fixes and will not last.