1. The reason Mark called Mary yesterday is "that" he needed to ask her a favor.
2. The reason Mark called Mary yesterday is "because" he needed to ask her a favor.
3. The reason Mark called Mary yesterday is "so that" he needed to ask her a favor.
I think that #1 is grammatically correct, and I'm not sure if #2 is grammatically correct, but it can be used informally to mean #1.2. The reason Mark called Mary yesterday is "because" he needed to ask her a favor.
3. The reason Mark called Mary yesterday is "so that" he needed to ask her a favor.
I don't think that #3 is correct.
