Syd, the expression 'Care meeting" is probably confined to those who followed JT's ministry (though I am willing to be corrected). My understanding is that it is a (monthly?) assembly* meeting where suggestions are made as to how the meeting's weekly (or special) collections should be distributed, in other words, to 'care' for those in need (Acts 6:1 and 1 Tim 5:16). After widows etc, gifts for the Lord's servants would be considered as well as any other special expenses.
* I say 'assembly' meeting as it was later attended by sisters as well as brothers but it was not considered to be on a par with other meetings of the assembly,