When entering the Form 1099-R reporting the $150K distribution exactly as on the form provided by the 401(k) plan, you should have indicated that you moved the money to another retirement account (or returned it to the same account), that you rolled over part of the money and that you rolled over $140K. The result would have been $150K being included on Form 1040 line 16a or Form 1040A line 12a, $10K included on line 16b or 12b, and the word ROLLOVER next to the line.
Also, the IRS has no knowledge of a rollover back into a 401(k) account other than what you tell the IRS. A 401(k) plan does not report receipt of rollovers.
Amendment should not be required if the IRS is correctly determining and assessing taxes on an unreported $10K of income, just pay the bill. However, you still might want to go through the amendment process to confirm that the IRS calculated correctly; they don't always do so. Also, if you entirely failed to report the distribution and rollover, the IRS would likely treat the entire $150K as taxable and you would need to amend to correct that. (If the IRS has knowledge of the rollover but not from you, perhaps the account is an IRA, not a 401(k). IRA custodians do report receipt of rollovers. If it's an IRA, the reporting would be on line 15 or 11 instead of 16 or 12.)