What behavior of Mr. Wickham’s (in regard to Miss King) does Mrs. Gardiner find odd?

Mrs. Gardiner finds it odd, not to say sinister, of Mr. Wickham to be paying court to Miss King after she's recently come into a large inheritance. This confirms Mrs. Gardiner in her suspicion that Wickham is an incorrigible gold-digger who simply cannot be trusted around young, eligible ladies.
At this stage in the story, Elizabeth has yet to be apprised of Wickham's villainy by Mr. Darcy who, in due course, will tell her all about his caddish and disreputable behavior towards his sister. But for now, Elizabeth defends what she sees as Wickham's prudence against Mrs. Gardiner's dire warnings of his far from pure intentions. It's only later on, when she reads Mr. Darcy's shocking revelations about Wickham's true character, that Elizabeth will finally see this importunate rake for what he really is.

Elizabeth likes Mr. Wickham so much, and Mrs. Gardiner trusts the judgment of her sensible niece. So when Mr. Wickham abandons his attentions to Elizabeth and begins to pay more attention to Miss King, a young woman who has just inherited a large sum of money, Mrs. Gardiner says that she "'should be sorry to think [their] friend mercenary.'" She fears that, perhaps, Mr. Wickham is now only paying attention to Miss King because of her inheritance of ten thousand pounds. Elizabeth, however, seems to find this concern somewhat problematic. Her aunt would call such an interest a mercenary one, but Elizabeth suggests that it might actually be more "'prudent.'" In the past, her aunt cautioned Elizabeth against marrying him when neither of them have any money, but now she criticizes Wickham for his interest in Miss King because she does have money. Elizabeth is, of course, keen to defend the man she believes to be her friend, but there is also some truth to what she says.

In chapter 27 of Jane Austen's Pride and Prejudice, Mrs. Gardiner asks Elizabeth about Miss King, who is now Wickham's love interest. Wickham, who was presumably courting Elizabeth before, is now seen courting Miss King. Coincidentally, Miss King just inherited a large sum of money, which makes the intentions of Mr. Wickham all the more suspicious. Already, Mrs. Gardiner has an opinion of Wickham. She thinks him a "mercenary."
As such, Mrs. Gardiner wants to know what kind of girl Miss King is in order to determine the type of man that Mr. Wickham really is. The result is that, according to Mrs. Gardiner:

[Wickham] paid [Miss King] not the smallest attention till her grandfather’s death made her mistress of this fortune.

Therefore, Mrs. Gardiner's assumptions that Mr. Wickham is only interested in people for what he can get from them are correct. Wickham is attracted to the ten thousand pounds that Miss King brings to the relationship, while caring very little about the woman herself. He is quick enough to drop Elizabeth, even when they were getting along well. Soon enough, Elizabeth will see the extent of Wickham's wickedness when he diverts his attention to someone else: her sister Lydia, whom he disgraces.