It gives them a -50% penalty to their attraction value, though some people are reporting that it doesn't actually apply for them. Essentially, if it works as designed, their projected size (pops randomly select ethos to flip to, so this won't line up with their actual size) is half what it would be if you weren't suppressing them. So they'd theoretically be size twelve now if you weren't suppressing them.
To get rid of them, find the ethos they're based on and mouse over its attraction value to find out where it comes from, then work to lower it while raising your attraction for ethos you like. However, this might be a doomed endeavour; actually zeroing out an attraction value once it's gotten started is near-impossible.
General rules: your governing ethos have a base attraction, which can be boosted by buildings, ruler traits, and policies. Also, once a faction is active it exerts its own attraction value. If you've got certain government types that can lower attraction for some ethos and raise it for others.
Xenophobes: attraction from enslaved alien pops and repugant aliens on the planet. Attraction from fighting aliens and from aliens committing atrocities against your species, reduced attraction from leadership of other species and free xenos.
Xenophiles: attraction from free alien pops and charismatic aliens on the planet. Attraction from allowing alien leaders and migration treaties. Reduced attraction from repugnent pops and atrocities against your species by other empires.
Militarist: attraction from being at war or losing wars and having hostile/rival neighbors for pops with full citizenship or who can provide military leadership. Attraction from all strong pops. Reduced attraction from lengthy peace
Pacifists: attraction from being at peace for long periods and no hostile/rival neighbors
Spiritualists: attraction if you have psionic research or ascension perks and for defensive pact/fed with spiritualist empires. Reduced by having or being robots and by AI rights.
Materialist: attraction from AI rights and having/being robots or cyborgs, and from research pacts with materialist empires. Reduced by psionic research and ascension perks.