The US Embassy in the UK's website specifically excludes even British non-citizen nationals (BOTCs, BOCs, BNOs, British subjects and BPPs) with British passports from applying for ESTA. So a Refugee Travel Document issued by the UK will also likely not count.
If the airline incorrectly assessed your ESTA status, they may owe you involuntary denied boarding compensation. But if your ESTA is actually listed as pending, then all you can do is wait for it to be re-approved or apply for a visa and try again.
The processing time for a travel permit (Advance Parole) currently averages 5-24 months, depending on the service center processing your application. USCIS provides a database where you can check the most current processing times, updated once per month.
Electronic Travel Authorizations (ETAs) operate slightly differently than the E-visa. An ETA is a digital travel permit that allows foreign visitors to register electronically without the need for a traditional visa.
It is commonly used for re-entry by people in the process of applying for permanent residence, applying for a status adjustment, or applying for asylum. Refugee travel document - You may be able to use this document to re-enter the U.S. if you have refugee or asylum status.
The travel authorization document authorizes TPS beneficiaries to travel, but the decision to admit someone into the United States is up to the discretion of a CBP officer at a port of entry. That could be either at the border or an airport. Certain circumstances may heighten the risk of being denied entry.
ESTA approvals are typically granted for a two–year period or until the applicant's passport expires, whichever is sooner. ESTA provides validity dates upon approval of the application. Therefore, a traveler must apply for a new ESTA when the prior ESTA approval or passport expires.
A Travel Authorization (TE) is used to request approval for a business-related trip. In this document, the traveler indicates trip destination(s), purpose, and dates of travel and requests advance checks. In response, the TE records trip information and schedules advance checks.