Nice rifle, though I see nothing to suggest postwar (interwar)?
I have yet done a satisfactory trends sheet on the modifications (TD & grips), though I can say they are not typical this early, - neither of them, though most interwar/republican era rifles were modified with a TD. At least in most cases, there are exceptions with the 98a, while the G98 almost universally received the modifications, some 98a police types didn't, PwB for instance. Whether this is related to police service, where such features are less necessary or desirable (waste of time for the ordnance shop) or related to the more secretive nature of all things police (the IAMCC and related "ambassadors" were routinely scrutinizing and nitpicking every element of police structure and operations); or possibly in the case of the PwB, a case of squirreling away rifles, but most I have recorded lack modifications although are property marked.
Regarding the MG marking, Craig (CB) owned 1917 Erfurt 9905 b MGSSA.29.3.K.30, though largely matching, it sold soft at Amoskeag when they sold off much of his collection. Like $800, but when a large collection is dumped prices sometimes suffer due to volume and limited collectors/available funds. Craig reported the marking across the BP face, though I have no picture of it. I am sure it was like yours or the more common horizontally applied, which is more common than vertically. Of course Jeff Noll is the go to guy on these, he has a thing for MG related, but so far as i have seen, these are very rare, but that is true of any unit marked wartime 98a, but these rifles tend to be desirable and rare, a good combination!
** Another interesting thing about this rifle is its proximity to another of CB's rifles, one he had a special project regarding, he was working on the subject when he passed away and we spoke of it often. His rifle, 1917 Erfurt 1947 d, buttplate flat marked G.A. LAUF, which he attributed to a security role for the dam at border with Laufenburg (Switzerland), he wrote a brief outline of an article he was working on, never finished it so far as i know. Apparently, the Germans discovered a French plan to blow up the power plant which powered both Swiss and German industrial works in the area, the Germans naturally established a military presence, mostly armed with 98a and Reichsrevolvers apparently, as a few have been noted with these markings. I doubt the threat was very credible, though the Germans had to take precautions all the same, I can't see risking relations with the Swiss over such a trivial target, the Swiss would have taken it badly for sure and the the Swiss were no push over, both militarily and economically, hell in WWII they were the only country to still back their money with gold (in real terms) and the Germans needed them so much they left them alone, even Stain supposedly stated the Swiss were off limits when they took over Europe. Anyway, I need to try and weave something together from the draft article and his emails on the subject. A worthy subject and something that interested CB...
*** Also, I am working on trends for the 98a, both RR acceptance and TD/grips introduction, but Erfurt seems to have been slow to introduce either feature, far behind the rest, even tardier than Danzig, though I am hoping there is more consistency when it was introduced and not erratic like with many of the other factories. I should have started where TD-grips are known and worked backwards... but i started from late 1916 and am working forward, which so far means consistency in lacking both!