Anyone have any idea of how paying back sign on bonus works?

I left my old firm the year after I joined it and was required to pay back my sign on bonus in full amount although I only received the post tax portion. I was told that I would be able to recoup the taxed portion of that bonus once I received an amended W2C showing an adjustment in my taxable wages after my original taxable amount had the full sign on bonus amount taken out. However, I'm not familiar with how the tax for this works. Has anyone gone through a similar experience like this?

It's causing me a massive headache since the first accountant I went to could not help me.

Thanks.