401K withdrawal

I just changed jobs and am going to cash out one of my supplemental 401ks because I really need it (life event). That account is 80% a Roth 401k and 20% is traditional. The retirement firm is requiring a mandatory 20% hold of my funds for taxes; however, I won't have to pay taxes on the 80% that is Roth, only an early withdrawal fee. How do I recoup the majority of this 20% they are withholding?