I have three tools I use depending on the clip. When it's a loop like that I have a quality flat blade that fits them snuggly. When they are a hook that a flat blade easily skips out of, I use a hex drive socket, but you'll need to find one that isn't too fat between interior and exterior. A piece of metal pipe 1/4 to 1/2" inch also works. Then those that all they seem to have is a hole, either the upward hook or loop isn't well formed, I stick one jaw of needlenose pliers in there, and push downward and outward...
... there's this one REALLY convenient 4 in 1 driver I've got that has double ended 8mm drive bits, small and large flat and crosspoint, and a double ended socket/sleeve that comes out of the handle, so you can quick flip between two bits inserted either way round. Anyway, this thing has the large bit suitable for the loop, the socket/sleeve works on the hook, and "most" of the just a hole type I can manage with the small flat which wedges in.... unfortunately it's a tool that seems extremely convenient for everything, and technically not actually mine (Subsumed into household tools from predecessor households as it were) so I have to hunt it down all the time if I want to use it.
edit: Oh they're still a thing, think you can get them from Ace Hardware in US... I should order half a dozen... https://www.millerindustrial.com/ace-phillips … rewdriver-8-in/
Unicorn herding operations are proceeding, but all the totes of hens teeth and barrels of rocking horse poop give them plenty of hiding spots.