In the top picture, the sticker indicates that the F31 recall was performed.
Can't quite make out the numbers on the bottom recall sticker.

The top # is 56044737AJ is the part # for a transmission control module and I think that's the same number as the one on the bottom of the 2n sticker. Why that appears twice with different dates I have no clue

The 1st # on the 2n sticker appears to be 56044?62ce but I cannot find a corresponding # in the parts fiche.

I suspect this relates to the F-37 reprogramming of the ECU to reduce HP and torque and the TCM to change the shift points plus check the torque converter. Essentially detuning the engine/tranny to protect a weakish torque converter.

A dealer should, for free, be able to pull up the vehicle data sheet and tell you for sure. Also you can go to the Jeep web site area for owners and with our VIN see if there are any outstanding recalls.

Definitely maybe they replaced the TC or maybe they did not. The first few 05 CRDs came with a TC that had some sort of plastic part the destructed shortly after leaving the lot so all of those got replaced under F-37. All other CRDs that went thru F-37 a) got an ECU detune; b) were supposed (I say that because in some cases for whatever reason this step was not always done, I know as I had one - if this step was done then your final shift point was raised from ca. 58mph to ca. 62mph) to have the tranny shift points changed; and c) the TC was "inspected" presumably by a test drive and only replaced, with a stock TC not the Euro one that came out in 07, if necessary.

Your very 1st priority is being sure the timing belt job has been done and when. All else comes later.

As to your torque converter. Chances are that it's the stock CRD TC (not the very early 05 one but the one used from after that to the end of the 06 model run). Whether or not it was replaced as part of the F-37 really doesn't matter unless you can find a record that somehow, extremely rare but not unknown, the service was done after the 07 models came out and the TC was "accidentally" replaced with a Euro TC. IMHO if the TC that's in there now doesn't shudder under load then at most you need a fluid (ATF+4) and filter change after which drive it and service it until it fails at which point upgrade to a Euro or Suncoast. No need to swap out now unless you have $s laying around or get the GDE stage II turbo like I did.

If and only if you confirm the TB job has been done then I'd get a GDE ECU tune of your choice, the EcoTune is a good one and my son's 06 quite happily did a cross country run fully loaded inside including 2 adults pulling ca 2,500 lbs of loaded Uhaul trailer with that tune. The GDE TCM tune is nice in that it restores the pre F-37 shift pattern but won't produce much mpg gain unless you spend a fair amount of time driving below 57mph. I'd put off the TCM tune until you have done more obvious things like Samcos, brakes, tires, airbox to turbo hose if torn on bottom just in front of turbo, etc.

Thank you. Annual emissions inspections are required so I need to be careful about how I modify this truck. Will the GDE Eco tune be okay? The one that reduces the power when in torque converter lock up?

I have the cash to do whatever it needs and the tools and time to get it done right. So throw it all at me. This is going to be a daily driver for work. Reliability and economy are most important. I don't expect to do much off road driving if any. Maybe wet grass or dirt.

Do you have an online supplier that you recommend for the motor mounts? Motor mounts are definitely on my menu. I can tell that these are shot.

Shocks, brakes, tires, alignment, tranny fluid, transfer case fluid, front and rear diff. I'm on deck for all of it.

Sort of depends on what you mean by treated right. Assuming you religiously follow factory service recommendations (mileage/time/fluid types) and fix things that wear out on a regular basis then life span can be a long time. Steps you can take to make it a longer time include a GDE ECU tune that, among other things, substantially reduces soot input to the intake system and replacement of the ceramic glow plugs (tips are somewhat prone to breaking, if you get a glow plug CEL replace immediately, and causing bad things to happen to the engine/turbo internals on the way out thru the exhaust). Generally, no flaming please, I'm not a big fan of asking any vehicle to do things it's not designed for, yes I know I have a "hot" turbo but I don't push it much, so I'd recommend against trying to hot rod the CRD or turn it into a monster off road Jeep, there are better platforms for both actions.

Life well up into 6 figure mileage is certainly possible if not probable on the other hand my cherry new off the dealer lot to me 05 CRD sport was totaled at ca. 16,400 miles because I stopped for the red light and the medium large dump truck with a load of 6 or so yards of dirt that was behind me did not stop. Engine still ran and tranny would engage but...

How long do these engines and transmissions last if treated right?