Doesn't "ei" mean "they"?
"ei" is indeed the nominative/accusative third person plural masculine personal pronoun. BUT, it's also the genitive/dative third person singular feminine one... In this sentence, "ei" is in the dative case.
Why is ei there at all?
Why is this not 'she gives them a turkey?'
'She gives them a turkey.' = 'Ea le dă lor un curcan.'