My wife has a Philippines passport and a green card and a dependent military ID card from the US. We have a flight that lands in South Korea (we have to claim our bags and recheck them on a different flight the same day); the flights are not connecting and are on two different reservations. We are not leaving the airport. Does she need a visa?
If collecting baggage, you will be "leaving the airport", meaning you'll cross the border.
As stated in Timatic, the database used by airlines:
Visa required, except for Nationals of Philippines with a [Green card] if holding confirmed onward tickets on flights departing within 30 days; when
-arriving from USA, departing to a third country (e.g. USA-ICN-PVG); or
-arriving from a third country, departing to USA (e.g. PVG-ICN-USA); or
-arriving from a third country after having transited that country for a maximum stay of 3 days, departing to USA (e.g. PVG-SGN-ICN-USA); or
-arriving from a third country, traveling to another country and staying there for a maximum stay of 3 days, then departing to USA (e.g. PVG-ICN-SGN-USA).
So if any of these conditions apply to your wife, she does not need a visa.