Lol they'd immediately know you're checking their profile if you liked an old photo of them. In Instagram this is often a mistake when you check someone's profile. You're just scrolling through their photos then you're phone's screen suddenly thought you double tapped a photo because of how you scroll through. You can unlike the photo but if they are online or their phone is connected to the wi-fi, they'd receive a notification about it even if you unlike it, haha.
