Per p. 335 Tactical Operations, "naval tug operations may only be performed in space." That sort of nixes WarShip recovery from planets.
Skipping past that, there's several practical issues to consider before lifting a WarShip from a planet.
First, per Total Warfare p. 78-80, out of control (e.g., crashing) WarShips would take 250 standard points of damage per point of velocity to the nose when crossing the space-atmosphere interface row. Orbital velocity over Earth is about 26 hexes per turn. A WarShip destroyed in a high speed closing engagement as it approached a planet might be moving at over 1000 hexes per turn. There's a good chance the WarShip will be confetti showered over the landscape.
The descent of a WarShip in atmosphere is one atmosphere row per turn, during which (per p. 79 TW) it only slows by 1 hex per turn. If it exceeds the safe velocity of a rows, then per p.79-80 it takes an additional 5 standard points of damage per point of velocity over the safe limit. An orbital velocity WarShip might still be moving at 20 hexes per turn when it passes into row 1 and the ground row. That's not a lot of damage compared to capital armor, but a WarShip doesn't crash because its armor was in good shape.
The final crash (p. 81 TW, p. 63 SO) does a relatively modest 2d6 x 10 x Velocity standard points of damage, but the average result is about 1400 points (140 capital) for a WarShip that started at orbital velocity.
So, there's a good chance you'll only have metal confetti waiting for a tug, or salvage freighter DropShip. But if you get past that issue and have a relatively intact WarShip on a surface, then you can start considering the problems of lifting it.
There's a matter of lift orientation. Space tugs push; the tug needs to be under the WarShip to get it off the ground. Even if it can hover over the WarShip and pull it up, there's the issue of fusion engine proximity damage to anything underneath the Spheroid DropShip (p. 88 TW). BT isn't a game of anti-gravity and harmless glowing engines like Star Trek; a crashed WarShip with a tug over it would want to pull a
Wall-E. ;)
Then there's a matter of capacity. A 100,000-ton DropShip tug with 12 safe thrust (about the max you can manage and still have tonnage for the frame and other necessities) still needs 2 safe thrust to lift off from a 1G planet (p. 88 TW), meaning (per p. 335 TO's thrust recomputation) the tug can only push small wrecked WarShips into orbit - nothing over about 500,000 tons in 1G.
WarShips under 500,000 tons are the ones least likely to survive entry since they don't have much armor.
But if you stretch the definition of "space" to include a vacuum planet (that's not the intent of the TO statement, though), and the WarShip landed at low velocity then it's probably intact and you might find a way to load it onto the nose of a tug and push it into orbit.