While copying from 𝓞 into 𝓟, Oliver Cowdery initially wrote that before the subordinate conjunction after, but then almost immediately he corrected the word order by crossing out the that and supralinearly inserting it after the subordinate conjunction (there is no change in the level of ink flow). The preceding that in the clause “that he should heal the nations” probably played a role in Oliver’s initial misinterpretation. Of course, he may have also been unconsciously avoiding the archaic construction “after that”. The same kind of error in word order occurred later on in the text, once more as Oliver was copying from 𝓞 into 𝓟:
For both 2 Nephi 25:20 and Ether 6:2, Joseph Smith later removed the archaic that which followed the subordinate conjunction after. The critical text will restore the original usage here and elsewhere; for further discussion, see under subordinate conjunctions in volume 3.
Summary: Maintain in 2 Nephi 25:20 Oliver Cowdery’s corrected reading in 𝓟 (“after that they had been bitten by the poisonous serpents”).