After a bit of searching, the only remotely Greek-based altlang I've found is Eressilian, which is mentioned only in the above Reddit post. It claims to be the result of the evolution of the Hittite language, after mixing with other languages in the region surrounding Asia Minor. These languages (notably Persian, Arabic, and Greek) mainly contributed loanwords, which were then modified and incorporated. Unfortunately, little information is given, and there's no substantial vocabulary list. The only supposedly "Greek" word given is adelphotés, which - matching sentences word for word - seems to have been turned into elelpulush. I haven't been able to determine its meaning or origin.
Some notes on Eressilian:
- The Hittite language was an Anatolian language, which may or may not be "daughter languages" in the Indo-European family. A competing hypothesis is that it is instead a sister language family, developing separately, rather than a branch.
- The modern Greek language is a Hellenic language, definitely Indo-European; Persian is also Indo-European, an Indo-Iranian language. Arabic, on the other hand, is an Afroasiatic language, not Indo-European. This means that there any purely Hellenic influence will be reduced.
- Eressilian's notable loss of grammatical gender is likely a Persian influence, not Greek.
In short, Greek influence on Eressilian is largely only through loanwords, and is not shown in grammatical structures. It's there, but it's minor.