Inspired by allied-hero's headcanon about Frank getting Trapper sent home while Hawkeye was on R&R.

It had been in his possession for a while.

He'd found it after Trapper's drunk leaving celebration in the Swamp, when Frank had gone back to get more of his things moved into his new tent.
McIntyre was sprawled across his cot, a nurse laying there with him and on Pierce's bunk was a piece of paper, all screwed up with some messy scrawl on it.

He'd read it. Trapper's leaving note to Hawkeye. About how important Pierce had been to him while he was there and how he wasn't sure how he'd be able to live with himself being safe back at home while his friends remained behind. He told Pierce that he didn't think he'd write, but Hawkeye was welcome to write any time and he'd try and write back.

It made Frank feel envious that there was no drunken note left on his bed. He looked anyway. Even checked the floor beside the bed in case it had fallen off. Nope. Nothing.

So he kept Pierce's letter. Knew it was wrong.
He felt a little guilty the next day when Trapper was woken late by Radar and told he needed to leave to make his flight.
Trapper panicked packing his last few things and Frank saw the genuine sadness that washed over Trapper when he looked at Pierce's bunk and that there was no note there. The nurse he was with shrugged, couldn't remember a note either and Trapper assumed it was a dream.
And now there was no time. He passed his goodbye to Radar in the form of a kiss on the cheek and then he was gone.

He kept the note in his pocket, folded away so no one could find it.
There were moments where he felt he should give it up. After Colonel Potter arrived and he was back in the Swamp Pierce would talk to BJ about how he missed Trapper. Hunnicutt often tried to lighten to the mood but it was clear that Pierce was in a rut.
Henry's death and Trapper leaving so soon afterwards had knocked him.

Frank knew that the letter, even being delivered a few weeks after Trapper had gone home would probably help lift some of Pierce's sorrow.
So he planned to hand the letter over later that day. Wait until Hunnicutt was in post op, but as fate had it, they ran into one another before that. In the mess tent, Pierce came over to him, bloody scrubs still on and chewed him out for being a lousy incompetent doctor and for almost killing a patient with his lack of care.
And it wasn't the first time he'd pulled a stunt like that but this time, the mess tent was full and Frank heard a murmur of agreement from some of the others in the room.
As quick as he was there, Pierce had left and he was there, shamed by Pierce again. And the letter burned in his pocket.

He finished his meal as though Pierce's words didn't bother him but they cut right through. Pierce seemed to forget that he was as human as the men he defended. Everyone else came before Frank Burns though. When he finished, he went back to the Swamp. No one was around. Presumably Pierce was in post op checking over all of Frank's patients and he'd seen BJ still in the mess tent.

He pulled out the goodbye note. He'd felt bad about holding onto the note up until then. Not any more.

He threw the note in the stove and lit it.
And he chuckled to himself as it burnt.