Given that the check was made out to your new company's plan for your benefit rather than to you personally, the bank should not have permitted the check to be cashed, but they did it anyway. You effectively transformed a direct rollover into payment made to you, so the distribution no longer qualifies as the direct rollover reported on the Form 1099-R issued by the old employer's plan.
To be able to complete an indirect rollover of this distribution you would have to self certify to the new company's plan IRA Rev Proc 2016-47 that the late rollover would qualify for a waiver of the 60-day rollover deadline. However, none of the reasons listed in the Rev Proc really applies to your situation. The closest seems be reason 3.02(2)(c), that the distribution was deposited into and remained in an account that you mistakenly thought was an eligible retirement plan. Unfortunately, I suspect that you knew that the bank account to which you made the deposit was not an eligible retirement plan, otherwise you would have completed the rollover indirectly in a timely fashion if that was your intent.
Note that self-certification is not actually a waiver, so the IRS has the option to determine in the future whether or not the rollover was a valid rollover. Given that money was deposited into your checking account, I suspect that the funds got used for other purposes even if only temporarily, so would not actually qualify for a waiver.
https://www.irs.gov/pub/irs-drop/rp-16-47.pdf
