If you roll the offset distribution over to the 401(k) at your new employer, you'll need to provide explanation with your tax return for the year of the offset distribution since 401(k) plans that receive rollovers do not provide anything to the IRS that documents receipt of a rollover contribution. If the rollover is instead to an IRA, the IRA custodian will report on Form 5498 the receipt of the rollover contribution, so no separate explanation would be needed.
