Can I travel internationally while my green card is being renewed?

Yes, you can travel if your green card has expired and you have a receipt notice showing you filed Form I-90 to renew it.

After filing Form I-90, USCIS issues a receipt notice (Form I-797) that automatically extends your expired green card by 24 months.

U.S. Customs and Border Protection (CBP) should accept the combo of expired green card and I-797 at the airport or land border.