The Scythians raided Eastern Hallstatt to death. Then some of the locals transitioned into a Thraco-Scythian cultural mode, and these fought more incursions off, but raided themselves even deeper into Central Europe. So a lot of people got into close contact with "Scythian ways" either by direct, "real Scythians", or those which adopted the Scythian ways, the Thraco-Scythians primarily (like Vekerzug culture). Therefore through what remained of Eastern Hallstatt and the Thraco-Scythians, along the old communication routes along the Danube in particular, Scythian cultural elements and probably even individuals travelled to the now booming very Western fringe Hallstatt sphere, which became the centre of La Tene. Its also not just the La Tene Celts which adopted some of this, but also, but way more limited, the Germanics. It affected most of Central Europe a lot. It was a huge impact, like you find whole areas of the Lusatian and Eastern Hallstatt sphere completely destroyed or massively degraded, with, on some sites, thousands of arrowheads around fortified settlements which were burnt to the ground.
This brought the Eastern Hallstatt sphere completely down and the luck of the La Tene Celts and Phocaeans in Massilia was that they just used the sea route, because both the West Hallstatt fringe and the Greek world got only mildly affected, same for the Illyrian core, while everybody closer to Pannonia was severely affected.
It was similar to the Hunnic, Avar and Mongol incursions, which usually didn't reach much beyond the Danubian sphere, with exceptions here and there.
Compare with the Magyar raids:
https://upload.wikimedia.org/wikiped...landozasok.jpg
They came far, even to Iberia and Italy, but most affected was Pannonia and the Danubian sphere. The Scythian and Thraco-Scythian raids seem to have been similar in some ways, same goes for the even earlier Thraco-Cimmerians. They all left their mark, and contrary to the Magyars, they had some innovations in their package, especially concerning horse breeds, gear and metal working, weapons.