Can we all agree that an inherited 401(k) can be rolled over to an inherited IRA, without it being a trustee-to-trustee transfer?  She really doesn't want to roll it over to a Roth IRA, since that will still make it taxable.  The disadvantage to taking the distribution and then depositing it to a new IRA account, is that the tax has been withheld.  Would the payor accept return of the check with instructions to issue a new check to the IRA trustee?  

For less than helpful advice, you can check the Schwab website, which says "If your employer made your rollover distribution check payable to you rather than to Schwab, see our Rollover IRA common questions to find out what to do."  Just try to find that part of the website.  Maybe it was on the TD Ameritrade website, before the merger.