I'm not sure how you know that its wrapped in something, Fu. Did one of your characters do that and not post it? The only one who posted wrapping it was Alec (he wrapped it in his over shirt). It wasn't mentioned if Reece kept the covering on.
Here is the history of the Escafil with links where all this happened.
Reece scoops the box up out of the ground and cradles it in his arms. "Alright, we should go find the others at the space-ship and see if they need our help, yeah?" He smiles at Alec. "You've done way good, bro. Totally rad. Now you just need to take us to where the ship was- can you do that?"
http://animorphsforum.com/forum/index.php/topic,2657.670.htmlGM post:
Reece and Alec find the others at Jethsa's ship, although it was greatly complicated by Alec's refusal to slow down and wait for Reece. Reece was forced to run the whole way and arrives at the ship some what fatigued.
Reece's actions after that:
Reece stalls behind a few trees to demorph. As Miller's features melt away, he pauses for a breath. He'd rather not waste any more energy morphing again than he'd have to, so instead he enters the ship cautiously, hands in front of his face. He is greeted by the sight of his friends, the unknown human, and the unconscious Andalite.