Can my wife travel to India while her H4 extension is pending?

Hi,

My H1 visa is valid until Aug 2022 and after my change of employer with the visa transfer last year I received the I-797A which is valid till Feb 2025. My wife is on an H4 visa which expires in Aug 2022 and she had to travel to India in Oct 2022, meanwhile, I applied online for her H4 extension (Using the I-539 form) and submitted all the documents by paying extension fees here in the USA.

Can she travel with the pending H4 extension by herself?

Yes she can travel while her extension of status application is pending however she will need a valid visa to enter back unless she already has one. Otherwise she will need to go for stamping.