Beric Dondarrion & Thoros of Myr
These two, having unsuccessfully attempted to execute Gregor "the Mountain" Clegane on the orders of Ned Stark, helped form the Brotherhood Without Banners - a traveling group of mercenaries who had a measure of honor among them but also weren't averse to working for profit. They have multiple connections throughout the Eastwatch Seven (most of them unpleasant).
Thoros (Paul Kaye, a.k.a. the one with the man bun) fought in the Siege of Pike alongside Ser Jorah, some time before the TV series began. Since then, they've both turned their backs on knighthood. Gendry, as already mentioned, hates these two because they sold him to Melisandre for two bags of gold coins. They have no outstanding beef with him, and may even feel regret for their earlier actions. (Beric and Thoros, incidentally, are both on Arya's hit list for what they did to Gendry.)
Beric (Richard Dormer) once fought and lost to the Hound in a trial-by-combat after the group had captured him. But thanks to Thoros' repeated ability to resurrect him, Beric returned to life immediately after the battle. Much later, the Brotherhood encountered Sandor again, this time after he'd undergone a change of heart and was living amid a peaceful settlement. When the entire settlement was murdered, the Brotherhood invited the Hound to join them, and surprisingly, he agreed... ish.
Sandor "the Hound" Clegane
With no major beef against anyone in particular in this fight, Sandor Clegane (Rory McCann) nevertheless seems to dislike all of his companions equally. He's on the team only because — much to his own shock — he saw a vision in the Lord of Light's flames, warning of the dead marching on the Wall near Night's Watch outpost Eastwatch-by-the-Sea.
Sandor's got history with several of these men, but none more so than the family of Jon Snow. Back when Ned Stark was executed, Sandor was still Joffrey Baratheon's personal bodyguard, and was there at the Sept of Baelor when the beheading took place. Still loyal to the Lannisters at the time, he did nothing to intervene. That's -1 point.
Despite his own grumpy indifference, he nevertheless protected Sansa Stark more than once while she was being forced to stay in King's Landing. When he finally decided to break his vows and leave King's Landing for good, he offered to take Sansa along, and escort her back to her home of Winterfell (she refused). For probably his first altruistic act ever, he earns +1 point.
He later wound up traveling alongside Arya Stark, protecting and even mentoring her to some extent while intending to return her to her family in exchange for a reward (-1 for putting money first). The two of them began their time together with a mutual hatred, but gradually came to respect each other, and even grudgingly like each other — though neither of them would ever admit it. The proof is in the pudding, though: Arya at one time had the Hound on her kill list, but after her adventures with him, she no longer wanted to kill him. +1 for winning over someone who wanted him dead.
The math there adds up to 0, meaning he's got just as much going against him as for him. Should he survive the conflict near Eastwatch, there could be several incredibly awkward reunions in his future, if he makes his way to nearby Winterfell. And if Jon finds out about any of Sandor's history with the Starks, his indifference toward the Hound will change in a big way.
But if we're being honest, none of this matters too much; all we really care about is Sandor making it to Cleganebowl.
It's a good thing that Jon is the leader of this motley crew, because he's the one member of the team that has no major issues with any of the others. He's also the moral compass, the one who unfailingly will fight for the greater good of all of Westeros. Aside from leading these guys into battle on this insane mission, his job by default will also be that of peacekeeper. Holding these men together — an old friend, a new friend, and several peeps he's never met before — will be a serious challenge. To his credit, Jon tends to be at his best in difficult situations.
On the other hand, he may not have to work that hard to keep the peace. Trying to survive a horde of the undead that vastly outnumber you tends to make personal issues kind of trivial.