The mainstream of Greek was not influenced substantially by Hebrew. The Hebrews were just another barbaric tribe in Classical times, as far as the Greeks were concerned, and not a terribly important one. Greek did get some words from Persian (the word for “chore”, αγγαρεία, is still used); but the Persians had an empire: they were barbarians that the Greeks noticed.
Because of Christianity, Koine Greek did receive some Hebrew lexicon, but really, not that much: most New Testament writers made a point of translating things into Greek. The most enduring influence on Greek is probably the word for Saturday, Σάββατο, which is of course just Sabbath; and a swag of ultimately Hebrew names, like John and James.
The Greek that Jews spoke was of course a different story. The Greek of the Septuagint is at times awkward, in some part because it’s a literalish translation, in part because of Semitisms in the language. Some of the New Testament is quite learned Greek; but some is colloquial vernacular, and again there are expressions showing Hebrew and Aramaic influence. (More Aramaic.)
We don’t know enough about Judaeo-Greek, the now extinct Greek spoken by Romaniote Jews in modern times. The Judaeo-Greek Torah of 1547 was a word-for-word translation; being in vowel-pointed Hebrew script, it tells us a fair bit about Early Modern Greek phonetics, but nothing about any living language’s syntax.
But from what we do know, the relation of Judaeo-Greek to Christian Greek was not like Yiddish to German, and indeed few Jewish languages were as distant from their Christian counterparts: they were more like Jewish English, with some lexical loans from Hebrew, and maybe some archaisms from being separated, but otherwise identifiably the same language. As this article shows, codeswitching to Hebrew came in handy for secrecy—as indeed Greek migrants have done elsewhere.