If you want to be grammatically correct, (with an apostrophe before the "s") is the standard and widely accepted form.
While "Season’s Greetings" is the safe bet for 99% of situations, here is a quick breakdown of how to handle different contexts:
The reasoning is simple: the greetings belong to the season. In English, we use a possessive apostrophe to show ownership or association. Just as you would say "the winter’s chill" or "the year’s end," the greetings are a product of the specific holiday season. Why "Seasons Greetings" (No Apostrophe) Is Common
Because the greetings belong to that specific time, you need the apostrophe to show possession.