I think it is a bit of personal preference. In my opinion, it is better to omit "that" when grammatically possible. I would have written the sentence as: "Rumor has it that it is highly likely there is a great deal of gold inside ancient tombs and shipwrecks, so treasure hunters all gear up and are planning to get it before extreme weather comes along." I would leave the first "that" because two "it"s next to each other sounds awkward, but both are necessary for the sentence (unless we change the sentence structure a bit more). I would omit the second "that" because it sounds awkward due to the first "that" coming close before