Warranty for battery

The factory installed battery and any replacement battery installed as a warranty service are all covered by the warranty (up to the end of the warranty period) if they fail or if they meet Apple's standard for a "defective" battery. It would also have to be less than 500 cycles, as loss of capacity is considered normal with enough cycles.

iPhone Battery and Performance - Apple Support

A normal battery is designed to retain up to 80% of its original capacity at 500 complete charge cycles when operating under normal conditions. The one-year warranty includes service coverage for a defective battery. If it is out of warranty, Apple offers battery service for a charge. 

Like I said earlier, if there's a warranty replacement battery installed, that's still under warranty until the end of the warranty period, or 90 days from the date of installation - whichever is longer. A lot of Apple repair parts come with a 90 day warranty on the parts.

If your battery has failed or dropped to under 80% health (Settings > Battery > Health) it is covered.