The List of TMs that Rocket will award out for turning in rare Pokemon:
Sweet Scent
False Swipe
Echoed Voice
Frustration
Skill Swap
Embargo
Hone Claws
Endure
Thunder Wave
Fling
Smack Down
Acrobatics
Rock Polish
Bullet Seed
Seismic Toss
Rock Tomb
Infestation
Natural Gift
Pluck
Recycle
Shock Wave
Captivate
Attract
Roar
Toxic
Sunny Day
Ice Beam
Light Screen
Protect
Rain Dance
Return
Double Team
Reflect
sludge bomb
Rest
Payback
Swords Dance
Poison Jab
Swagger
U-Turn
Iron Tail
Teleport
Calm Mind
Hail
Bulk Up
Taunt
Roost
Torment
Facade
Flame Charge
Low Sweep
Steel Wing
Charge Beam
Incinerate
Volt Switch
Dream Eater
Power-Up Punch
Water Pulse
Whirlwind
Mega Drain
Fury Cutter
Silver Wind
Snarl
Shadow Claw
Will-o-wisp
Hidden Power
Dig
Psych Up
Quash
Venoshock
Energy Ball
Struggle Bug
Flash
Smart Strike
focus punch
sky drop
round
telekinesis
safeguard
Thief
Snatch
Aurora Veil
Frost Breath
Confide
Trick Room
Substitute
Sandstorm
Icy Wind
Stealth Rock
Explosion