Another answer from our community:
It's possible, in theory, for the authors of the Gospels to have been influenced, somehow, by Paul's letters. Realize, though, that Team Xerox and the Internet weren't quite as efficient as they are today; Paul's letters were sent to specific churches and individuals, who had them transcribed (enter Team Xerox :) ) and passed on to other churches (enter the early Internet :) ) by hand. More than likely the Gospel writers would have read Paul's epistles by the time they started their own writings.
Some close textual parallels suggest that each of the authors of the gospels may well have been influenced by Paul's letters. For example:
- some parallels have been detected between Mark and Romans. Mark's "he declared all foods are clean" ( 7:19) is considered to resemble Rom 14:14: "I know and am convinced in the Lord Jesus that nothing is unclean in itself."
- the eucharist in Luke 22:19-20 is based on Mark, but it differs in "my body which is given for you; do this in remembrance of me", which resembles 1 Corinthians 11:24-25. In fact, the eucharist in Mark 14:22-24 may also be based on 1 Corinthians, so that Luke was influenced both directly and indirectly.
- Whereas Paul, in his references to a risen body of Jesus, spoke of one that was spiritual and not flesh and blood [1 Cor 15:44,50], Luke was particularly insistent on the reality of Jesus' appearance. Luke may have been influenced, in that he rejected the Pauline version, rather than that he copied it.