Do i need to worry about a battery that appears to charge correctly but has a "Service Battery" warning?
"Do I really need to worry about this" is hard to answer.


If you need to be able to use the MacBook for long periods of time when not plugged in, then yes, you probably do, because the battery that you have is probably not reliable.
If you mostly only use the MacBook when plugged into A/C power, then no, you probably don't need to worry about it at all. It will most likely work just fine for that purpose.


Do keep an eye out to make sure that the battery doesn't start to bulge or anything like that. If it does, immediately remove it from the MacBook.

As an aside: MacBook batteries generally cost somewhere between $80-130, so I would be highly skeptical of the quality of whatever battery you bought for $20 off Amazon. Where by "highly skeptical" I mean "I would not leave it plugged in and unattended when I was not at home." Which is probably me being overly protective, but as the saying goes, "Better safe than accidentally burning down the apartment complex and/or neighborhood."