Regulus pulled back. He was willing to do the pursuing, but he would not beg, especially when Remus Lupin was involved. "I wouldn't use this to get you fired," he said, because that he understood well. The danger was real.
"Regardless, we're here to go over a lesson plan. We should do just that." No, he wouldn't beg, but he wouldn't give up this easily. He'd try again in the future, but for now they could do something else.