TL;DR According to various sources, they do not have a legal right to (further) reparations. However that was only possible because of some legal trickery.
In layman terms it went like this:
- 1953: Please wait with your claims until we are prosperous and can
pay them without inconvenience.
- 1990: Now that Germany is re-unified your claims have no legal basis
anymore. And it has been so long, let the past behind.
Whether they actually do or don't have those rights is for some court to decide - many reputable sources say no, so this is the best information currently available.
I'll try to separate the two claims - which isn't easy because it seems that there is some disagreement: The Independent says my point a) comes to the sum given in b), while other sources don't mention a) at all.
a) A forced loan for 476 million Reichsmarks (which given
various accumulated interest rates comes to varying numbers)
The highlighted part of the image shown above literally translates to
remaining debt without specifying what kind of debt (For completion: The top column just says
total sum given to the Wehrmacht - again not specifying what kind of debt).#
The Welt, quoting a Tagesschau interview, claims that it in fact wasn't a loan but occupation costs which were billed to Greece (It also claims that at the time this practice was legal by international law).
However in practice those costs were treated like a (zero interest) loan. Funds not used were given back and the fact that this money would be payed back was contractually obliged (however without a fixed due date).
Whether treating it like a loan converts it into one is, AFAIK, legally uncharted territory.
b) War reparations totaling $302 billion
I'm not sure about the methodology that lead to this number, however whether there should be war reparations has never been a question: The Allied Commission of Paris in 1946 decided that Germany must pay Greece $7.1 billion 1938 dollars.
It seems like this agreement denies the right to request further payments:
The Signatory Governments agree among themselves that their respective shares of reparation, as determined by the present Agreement, shall be regarded by each of them as covering all its claims and those of its nationals against the former German Government and its
Agencies, of a governmental or private nature, arising out of the war (which are not otherwise provided for), including costs of German occupation, credits acquired during occupation on clearing accounts and claims against the Reichskreditkassen (source)
Some amount has been paid to Greece - Bloomberg:
German postwar reparations included a 115 million deutsche mark ($66 million) payment to Greece in 1960 and $20 billion in payments linked to demands made at the Yalta Conference in February 1945, according to the German government.
Due to extremely bad experiences other countries had with getting reparations payments from Germany the London 1953 Debt Conference lessened the load on Germany (e.g. this, or a more complete study).
Article 5.2 explicitly states that further claims shall be deferred until the problem of reparations is settled.
Tricky Legal Part
The Treaty on the Final Settlement with Respect to Germany created a sovereign German state without any legal obligations to the previous states on that territory.
It explicitly is NOT a peace treaty -
Due to "economical considerations" there is "no interest" for a peace treaty, general secretary Friedrich Voss explained.
An einem "Friedensvertrag" könne man "aus finanziellen Erwägungen kein Interesse haben", erklärte Staatssekretär Friedrich Voss. (source)
It is true that there is no reference to reparations, but this is deliberate, as the summary note prepared by the French negotiators confirms: "The Moscow Treaty [The 2 + 4 Treaty] does not contain all the clauses of a peace treaty; and it does not bear the name. In particular it does not mention the problem of reparations. ..." (source)
The trick was only letting the CCCP, the US, UK, France and the two Germanys write the contract.
[a peace treaty would] necessarily empower the former war combatants of the Reich which is neither in the interest of the Axis nor the two German states.
Es „hätte zwangsläufig alle früheren Kriegsgegner des Deutschen Reiches als potentielle Vertragspartner auf den Plan gerufen […]“, woran aber „[w]eder die Vier Mächte noch die beiden deutschen Staaten […] ein Interesse [haben konnten]“
Recht zwischen Umbruch und Bewahrung: Völkerrecht, Europarecht, Staatsrecht: Festschrift für Rudolf Bernhardt