Well, everyone is confusing the rules around care home fees and the IHT rules. It's really too complex to go into but the two are not linked in any way at all.
I thought you could freely give £3000 a year, no problem, but if you die within seven years of giving a larger amount (over 300k I think) then inheritance tax is owed.
£325k, doubled if a spouse has died earlier as their band transfers. Plus main residence is ignored up to a certain value IF it is left to offspring.
The potentially exempt gifts are, yes, £3k (but note - these are still only ever potentially exempt, if the estate was borderline you'd need to document the circumstances very carefully), gifts higher than that, if the donor dies within 7 years are added back into the estate so the estate pays IHT on the amount after it is added back in (not the recipient). Also, it's not a straight 7 years, there is a sliding scale, I can't recall the exact details but it reduces within the seven years too.
Also there are potentially exempt gifts for specific things, like a wedding. AND regular gifts from income that do not reduce the donor's standard of living are exempt from IHT and do not get added back into the estate on death, no matter when death occurs. Hence my mother giving each grandchild £200pm.
It's really complex and most people only ever pick up the headlines and don't look more deeply into the rest.