If I have a recent travel history to a foreign country, will I be eligible for this cover?

Yes. You will be eligible provided you not have travelled to the countries listed in the “Travel Advisory on Home Isolation/Quarantine and restricted travel” issued by Ministry of Health & FW, Government of India as applicable on date of policy purchase, since 60 days prior to the policy inception date and any time after the policy inception date.

Travel advisories can be found here: https://www.mohfw.gov.in