GENEVA—The Syrian opposition delegation to the Geneva peace talks has gone to pains over the past week to overcome its image as a fractious organization mired in infighting, trying to present a strong and united front to the media, Western backers and Syrians back home.

The team, led by 44-year-old lawyer Ahmad Jarba, has come under intense focus at the first talks between any opposition representatives and the Syrian regime in nearly three years of civil war. They were pressured to unify by their Western and Arab backers,...