Don't Nords typically actually like restoration magic? Dialogue from Skyrim's guards typically or makes fun of most magic, but the only things they say about Restoration is that they respect it and Skyrim can always use more healers. Which makes sense both since it's a lot more straightforward and helpful compared to a lot of magic (doesn't aid in deception or manipulate people like Illusion magic, doesn't kill things like Destruction, doesn't modify the laws of reality like Alteration, it literally just heals people), and because it's often used by priests, which would naturally give it a more benevolent reputation and make it more familiar to Skyrim's inhabitants.
Oh this is just a Vilkas problem. He didn't take her seriously and had his guard down, and thus got defeated. His wounded pride denies help and pokes at her being a mage (regardless that she's just a healer) as a divider between them.
Any other Nord would have accepted her healing help, but for someone stubborn like Vilkas, not so much.
Any other Nord would have accepted her healing help, but for someone stubborn like Vilkas, not so much.