She begrudgingly puts them on

At first, Linkle entertained the idea of simply throwing the invisible outfit on overtop of her pajamas. That way, she would be completely covered, even to an audience that wasn't "pure of heart". Unfortunately, there was a singular complication that rendered that particular plan unviable. It was too damn hot!

The invisible garments were already uncomfortably warm for a tropical island. Throw a second layer of clothing on under that, and she would be putting herself at very real risk of heatstroke. After long and careful deliberation, Linkle reluctantly decided that her health was more important than her modesty.

In the privacy of her bedroom, Linkle discarded her pajamas and changed into the unseeable outfit, leaving only her underwear to protect her modesty from the impure. The underwear in question consisted of forest green panties with a subtle leaf pattern and a matching bra holding her C-cup breasts. Said bra, while providing some support, obviously favored aesthetic over function, and likely would not hold up to the strain caused by, just as an example, adventuring. But what were the odds of something like that happening?

The birthday celebration went surprisingly well, despite Linkle's current state of dress. It was just a small celebration, consisting only of Linkle, her Grandma, and Aryll. Linkle's Grandma could apparently see the elusive fabric, and Aryll, despite a burst a laughter upon first sight of her scantily-clad sister, largely ignored the elephant in the room. In fact, it went so well that Linkle herself forgot about her undressed state, which was probably how she had ended up outside with Aryll, watching the clouds. At least until a giant bird appeared and dropped what appeared to be a girl into the forest on top of the island. That place was dangerous!

Linkle, filled with adrenaline, rushed to find herself a weapon so that she could help the girl.