Usually visa or ESTA would have been denied if LPR applies for them. Who in Greece told her she cannot enter the US on her green card? What authority do they have?
If she didn't formally give up her LPR status she should exit the US and re-enter as a LPR on green card.
Did she keep any ties to the US? E.g. lease or real estate, bank accounts, immidiate relatives such as husband or kids?
Also, green card is for living in the US, not yearly visits. What is her long term plan? Is it to live in the US? If not, then she's in danger (already is) of losing her LPR status. If she loses LPR (green card taken away), she would have to apply again whichever route she can use: marriage to US citizen, work, DV lottery etc.