"the two Earls put themselves in Arms; which being discerned, that business was prosecuted no further,"

"the two Earls put themselves in Arms; which being discerned, that business was prosecuted no further,"

does this mean:

"The two Earls aimed at each other; which being made aware of, business was prosecuted no further"?

What does "that" mean here? It seems that it doesn't have any meaning and can be left out.

Full passage below.

Humphrey V., Earl both of Hereford and Essex as the son of this illustrious heiress, officiated as Marshal of the King's house at Henry III.'s marriage in 1236, and three years later was one of the nine godfathers of his eldest son. "The custody of the Marches of Wales was committed to him, and he acquired the truly honourable distinction of the Good Earl of Hereford from his zealous opposition to the arbitrary measures proposed by the King."—Duncumb. Twice already he had protested against them; once in 1227, when he "demanded the restoration of the Charter of Liberties;" and again in 1253, "when that formal curse was denounced in Westminster Hall against the Violaters of Magna Charta, with Bell, Book, and Candle."—Dugdale. When the Barons' War broke out, he and his two sons were foremost in taking up arms against the King; and the eldest of them, Humphrey VI., was one of the chief commanders at Lewes, and again at the disastrous rout of Evesham, where, "it is said by some, that when he came near the place of fight, he withdrew himself." Be this as it may, both he and his father were taken prisoners; and while the Earl was pardoned and restored within the year, the son died soon after in captivity at Beeston Castle in Cheshire, whither he had been carried. Faithful to the family tradition, he had taken to wife an heiress of the best blood in England, Eleanor de Braose, the daughter of the Lord of Brecknock, by Eva, one of the five co-heirs of William Mareschal, Earl of Pembroke; and their son, Humphrey VII., inherited the Earldom at his grandfather's death in 1275. He and Roger Bigod were the two bold Earls who, in 1296, when ordered out to take the command of the army in Gascony, declared they would go if the King went, but not else; for, as Lord High Constable and Earl Marshal of England, they were bound only to attend upon the Sovereign himself in war. To assert their privilege, "the two Earls put themselves in Arms; which being discerned, that business was prosecuted no further."—Dugdale.