As a Greek citizen myself, it is well known that Greek government or airport employees can barely answer competently on questions regarding Greece’s own bureaucratic processes so why she chose to believe a random Greek person’s account of US immigration is beyond me. Also, covid lockdowns would not have prevented her from coming back to the US at any point. As others have mentioned, an LPR is not eligible for an ESTA and an LPR cannot split their time between the US and another country, and spend significant amounts of time outside the US without risking losing their status, especially without having applied for a re-entry permit prior to departure. A green card is for living permanently in the US, the ability to split time between two countries is only afforded to citizens.
Regardless, your relative needs to decide where she wants to live. If its the US, then she needs to exit the country, attempt to come back using her GC, and then stay here for a considerable amount of time before trying to leaving again (aka there are not going to be Greek summers in her near future as most expats do). If later on she wants the freedom to split her time between the two countries, she’s going to have to naturalize and meet the continuous residency requirements for that. Once she’s a citizen she can do as she pleases.
If on the other hand she wants to live in Greece, she can relinquish her GC and be on her way. Best of luck!