I’m not what you mean by the European Information Centre. Is it the Schengen Information System?
The Schengen Information System stores information on certain people which is then shared among EU member states. Here’s a list of why people would be recorded on it:
It says that people who have been returned are only recorded in the system since Autumn 2022. If you were deported 6 months ago, then it cannot be for this reason. I presume you are recored due to the first reason ‘refusal of entry or stay’.
You can request to see the information that is kept about you. If it is not correct, you can also request for it to be deleted. Here is a detailed article about this process:
The other issue is with the Greek immigration authorities. As you were deported, it is clear that Greece is responsible for your asylum case and refugee status. I do not see why an alert in the SIS would prevent them from issuing you with a residence permit as it concerns Germany and your stay in Greece is legal. It is possible that due to your extended absence from Greece, you have lost your refugee status there. As my colleague wrote, I encourage you to make contact with support services in Greece who will have a better understanding of the immigration law there.