If this original and new accounts were truly IRAs, it's rather improper that they did not permit a nonreportable trustee-to-trustee transfer (not a direct rollover), unless you placed some sort of time limit on completing the process. The term "direct rollover" only applies to the movement of funds between retirement accounts when either the original account or the destination account (or both) is an account in a qualified retirement plan (i.e., 401(k), 403(b), 457(b) or the federal TSP). IRA custodians who will not accommodate a trustee-to-trustee transfer are shameful and should be avoided as a matter of principle.
A proper trustee-to-trustee transfer done in the form of a check has the check made out to the receiving IRA account for your benefit, not just to the financial institution for your benefit. If the check is just made out to the financial institution for your benefit, you and the financial institution are free to deposit the check into any kind of account for your benefit, not just the same type of account from which the funds were taken. Technically that brings the funds under your control and precludes this from being a proper trustee-to-trustee transfer.
In your case the distribution was reported as a distribution from a traditional IRA, indicated by the fact that no taxes were withheld. (Rollover-eligible distributions from qualified retirement plans like a 401(k) are required to have a minimum of 20% withheld for federal taxes.) As a distribution, to make it nontaxable it must be reported as rolled over as SamS1 described.
The only problem with having to treat this as a distribution and rollover between IRAs is the one-rollover-per-12-months limitation. This rollover was not permitted if you did another IRA-to-IRA rollover in the period beginning one year prior to the date of this distribution and it prevents you from doing another such rollover in the one-year period following the date of this distribution. That's why you want to do nonreportable trustee-to-trustee transfers.
