There were a lot of these Turkish Meerschaums with the Kaywoodie style connectors sold to the Armed Forces during the '40's & '50's that were in country during this period. There are some that are still around today and are good Pipes for repair that should smoke well.
Steve Laug has reported good success with Murphy's Oil Soap, in both SF and Foundations, but he was not working with high grade Turkish Block. For the soft Turkish Meerschaum, the use of a soft tooth brush would most likely leave abrasion marks. I cannot provide information on this method with the Murphy's, because I've no experience with it... Using 600 grit wet/dry sandpaper, in a shallow dish of Everclear, works well on smooth surfaces. For rusticated and carved surfaces, the use of a soft white cotton cloth, as a substitute for the sandpaper, works but will require multiple attempts, allowing the Meerschaum to dry between these attempts, so that you can see what progress has been made. For intricate, undercut surfaces, the cloth can snag, so a doubled over Pipe cleaner will offer more control. The problem with this technique is that the patina will be lost, which is something that can take years to return. This method is something that I've come to learn to use in severe surface damage, as a last resort, because of the patina loss.
What I've learned is that Beeswax can effectively, but slowly (as there are no quick fixes) address many surface problems. When I started working on an estate Pipe (Battal's Dunhill Man) the first thing I addressed was removing the cake and cleaning the shank & bit with Everclear. This is also a multi stage process, as the Pipe must be smoked and then cleaned again, until it flushes the trash out of the Block. At the same time, before
I smoked it for the first time, I daubed liquid Beeswax all over the Pipe's exterior and then what was not absorbed, I melted off with a hair dryer, making sure that the Pipe was bone dry and with the bit removed. Years of grime, dust and part of the patina came off with the excess wax. It became obvious that a some point in time, the previous owner had put the Pipe in a smoke jar, because part of the coloring came off with the hot wax. This is not a problem, but instead part of the grime that needs to come off of the Pipe, so that the real coloring (the type that can only come from smoking the Pipe, with available wax to help) can occur. As I smoked the Pipe, I rubbed Beeswax on it, using the heat of the Pipe to melt the wax, which mostly was absorbed by the Block. After a dozen cleaning cycles and using this cold wax application to the Pipe, as it was being smoked, the Pipe was flushed and the surface was showing true coloration and patina. This method of Beeswax application will also work with rim char, by diffusing and spreading the carbon. It does not work with rim scorch, a condition that requires use of the Everclear and sandpaper. If you want, a light cleaning with a dampened white cotton cloth, using Everclear to dampen the cloth, can be used before the hot wax application. The thing to pay attention to in doing this is to keep in mind that this is only a light cleaning, that you might do to address gross debris buildup, so that you do not disturb the patina. Over time, I've learned that cleaning up estate Meerschaums can be a lesson in delayed gratification. I used to rush into removing surface blemishes with Everclear and wet/dry sandpaper, which works well and requires rewaxing. The drawbacks to this are the adverse results it can have on the Patina, which is the most time consuming aspect of bringing these Pipes back to their path of evolution. At present, I'm dealing with this same problem of 'ashtray marks' on a 24 year old Bekler. My approach to this is less aggressive than my past actions, as I'm doing the best I can not to disturb the Patina, which is starting to show more than it did when I first started working on the Pipe. Initially, I worked on these blemishes with a white cotton rag with Everclear on it, just enough to remove the surface grime, but not enough to draw the entire spot out of the Block. Before smoking it for the first time, I cold waxed the entire Pipe, paying particular attention to these blemishes, As I smoke the Pipe, I rub Beeswax on it, with attention to these spots. After a half dozen smokes, the Pipe is starting to show more of it's coloration and these blemishes are becoming diffuse, so that they are less defined. This technique seems to be better in the long run, as the Patina continues to develop more than if I'd used sandpaper. This method of waxing also works well with keeping the bowl plateau of a new Pipe from getting scorched, as the Beeswax works to spread the smoke marks as well as aid coloration and provide protection for the Block.