"Then why did you command it of me?"
"I did not command it. I told you to do what needed to be done, and left you to decide what that would be." Qhorin stood and slid his longsword back into its scabbard. "When I want a mountain scaled, I call on Stonesnake. Should I need to put an arrow through the eye of some foe across a windy battlefield, I summon Squire Dalbridge. Ebben can make any man give up his secrets. To lead men you must know them, Jon Snow. I know more of you now than I did this morning."
"And if I had slain her?" asked Jon.
"She would be dead, and I would know you better than I had before. But enough talk. You ought to be sleeping. We have leagues to go, and dangers to face. You will need your strength."
It's not important to Qhorin whether she lives or dies, she just can't come with them, but it's important to him to know what Jon Snow would do in a particular situation so that he may lead him effectively. Jon's actions are what allows Qhorin to formulate his plan of Jon pretending to turn cloak.
I really don't like the change, because you've completely changed the tone of the characters and introduced plot issues. When Jon finally makes it back to Qhorin he will be seen as unreliable, he was told to off some chick and instead he disappeared for days doing lord knows what, so Qhorin will distrust him. Which is completely opposite of what actually happens in the book. So now you need to devote screentime to that conflict and its resolution. I can't think of a single valid reason why they would make this change.
The problem in a nutshell is that Qhorin Halfhand would never trust TV-Jon with his final orders.