I just love how clear it is that Babs is trying to get caught here. She's got satellites. She's got Gypsy. She's got Helena. She's got Dick Grayson. She could stalk Dinah, directly or by proxy, for a decade and Dinah would never notice. But what does she do instead? She sends Kate, the sloppy noob who is, of her entire standard team at the time, the absolute least experienced at stealth and subterfuge (even Zinda has done more undercover). In other words, the one most guaranteed to get noticed, beat down, and dragged back to drop on Barbara's doorstep.
I said it at the old S_D, I'll say it again: it's the superhero equivalent of flicking paper footballs at a girl's forehead. "Hey! Pay attention to me!" So juvenile! Oh Babs. ♥