My prior employer paid me a retention bonus in 2018. I left that company a year later, causing me to have to repay half of the bonus. My new company added an equivalent amount to my starting bonus. I would like to not treat this amount from my new company as income, since it was simply used to reimburse my prior employer. My new employer did report this amount as income on my W2 and is not willing to recharacterize it.
What do I need to do when filing my taxes to avoid paying tax on this money that was basically passed through? What IRS regs describe the rules?