As with all airlines, you don't quote an ESTA reference since it's implied with a combination of your name, date of birth, passport country and passport number. The airline submits this data to the DHS, it sends an electronic tick if it finds your record. The airlines typically send a rolling and repeated data update until it gets a tick back. If TAP doesn't get the green light back from the USA it will show up at check-in stage. The usual problem is a recent ESTA expiry. But if you have a visa then this process doesn't use this electronic process, that uses an old fashioned human check of the visa print out, but during TAP's check-in process it simply says "no ESTA found".