Hm...
There's Egyptian influences on things like archaic period (pre-classical) Greek sculpture.
Religiously, hard to tell. The suspiscion is that the Greek mystery religions might have taken stuff from the Egyptians, but they were hardly alone in mysery relgiosity along the eastern Med. back in the days. And it was secret, enough so to make it hazy in retrospect exactly what was being taught.
As far as Egyptian high-brow theology, the Greeks apparently had No Clue Whatsoever. The sophistication of things like "The Memphite Theology" was obviously well beyond the horizon of the Greek of the day.
What otoh was directly taken from Egyptian religion was the notion of a happy afterlife. Looking at for instance ancient Mesopotamian conceptions of the land of the dead, it's a dark, dank, cold and dreary place. Being dead is not a meaningful state to Mesopotamians, it's just an eternity of tedium, everything is over. And that's also true for ancient Greek notions of Hades as the land of the dead, at least up to Homeric times. That's why the Greek dead drink from the waters of Lete, to forget who they were, once upon a time when it mattered. Or why dead Achilleus tells Odysseus that he would rather be a slave alive than king of the land of the dead.
And then suddenly there was this new surprise addition to the Greek afterlife — the happy fields of Elysion, where the dead live in eternal bliss.
The closest prior parallell to it was the Egyptian "fields of Iaru" (Ia=E, ru=ly, since the Egyptian "r" is a sound in between r, l and d), where the dead lie in the shade, having a cool drink, and watch the wheat grow ten feet tall and someone else do the work. Paradise...
So Greek took the happy afterlife from the Egyptians, and that's where the montheistic idea of a paradise after death comes from as well.
Thenthere's the indirect influence of alphabetic script as well, mediated by the Phoenicians.
The Egyptian system of writing was always a mix of alphabetic script and ideograhic signs. If one wanted to simply represent the sounds it was quite possible to go for phonetic script. The oldest Egytian tomb inscriptions tend to consider the pictures on the walls as sufficient ideograms and were much more phonetic than they later became.
As it turns out the alphabetic aspect of the Egyptian script was picked up by their semitic neighbours (oldest semitic language written in the Egyptian alphabet at the turqoise mined at Serbit el-Khadeim, Sinai penninsula), who did away with the ideograms as redundant, but adapted the alphabet, and then passed it on to the Greek.
As mentioned the Egyptian solar calender was the inspiration for the Julian calender, adopted and improved by Caesar, who actually inserted three extra months in one year to make things align properly. With a 15 month year he could get some extra campaigning in too.
Going by reputation from Greek sources, Egyptian medicine was much appreciated by the Greels as well, though it seems to be problematic to find direct evidence of borrowing.
As for direct political contacts between Egypt and Greece in classical times, there's quite a bit of evidence of it.
The kings of Egypt built a "treasure house" of their own at Olympus, like any other Greek polis would do, i.e. the Pharaos of Egypt found it to be wise policy to honour the god, the Olympian Appollon and his oracle, with gifts.
The reason for this of course being that Greek mercenaries and Greek armies were constantly passing through late dynastic Egypt. The Spartans in particular seems to have had a intimate relationship with the last Egyptian pharaos fighting the Persians. At the demise of independant Egypt, an entire Spartan army was fighting alongside the Egyptians, while the Persians had availed themselves of a "military advisor" in the form of a leading "Strategos" on loan from Athens.
