Pazyryk is thousands of miles from the Hellenic or Roman world - it's right by Mongolia and Xinjiang. And those interred in Pazyryk were Saka.

It's most likely a simurgh/śyenaḥ/mərəγō saēnō or a Huma/Homāio/Humay, which was a very common in Indo-Iranian culture

While Central Asia is now Turkic speaking, before the Mongol and Turkic invasions, it was historically Indo-European, as was seen with the Sogdian, Bactrian, and Khwarezmian.

The Greco-Roman myth of the griffin itself appears to have it's origins in the Indo-Iranian motif.

That said, the Pazyryk burials were from an era when the Indo-European migration was still occurring, so cultural and linguistics overlaps were still significant.