Can I travel internationally during the 60-day grace period after losing my job?

No. The grace period does not give you the right to return after international travel.

Workers in E-1, E-2, E-3, H-1B, H-1B1, L-1, O-1 and TN status who quit or lose their jobs have a 60-day grace period during which they can remain in the US and apply to change employers or switch to a completely different status. This grace period is intended to allow impacted workers a little extra time to try to find a new job, or to wrap up their affairs in the US before leaving. It does not include the right to return to the US after international travel. If you leave the US before your grace period is over, you lose the remaining days.