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?
Are both "îi" and "ei" necessary? Are they needed to make sure that this female person really is given a turkey?
Why is this not 'she gives them a turkey?'
'She gives them a turkey.' = 'Ea le dă lor un curcan.'