Is there a way to get from Murren to Chur ?

Murren connects by mountain railway to Lauterbrunnen. Here you can travel by regular train to your destination.

https://www.sbb.ch/en

Yes, you can easily get from Mürren to Chur, but it will take 4 - 5 hours and several train changes. You can see all the details on the bahn.de or sbb.ch websites. One of the easiest trips is a departure from Mürren at 07:36, arriving Chur at 12:43 (time 5H:07M, 4 changes). Depending on what time you leave Mürren, you may not arrive in Chur in time to connect with the Bernina Express (assuming you want to take the panoramic train, as it departs at 08:32), so you may have to spend one night in Chur.

We did exactly that trip 3 years ago. Easy answer for us was, we had a car parked in Stechelberg. Awesome drive. Some windy alpine roads as you come up from Brienz toward Luzern. Drove into Luzern for a lovely lunch on a patio on the river. Then through some alpine meadow countryside as you come down to the Zurichsee. Stopped into Liechtenstein and Feldkirch, Austria for short visits (just to tick those countries off our list; otherwise not worth the excursion). Into Chur by 5:00 to drop our car off. Took the Bernina Express the next morning (which is AMAZING by the way).

So my advice: rent a car and park it in Stechelberg. Its a bit of a waste to be paying for a car that is sitting in a parking lot, but for us worth the convenience later on (and frankly about the same overall cost as two train tickets).

The OP is on a tour, so will not be able to rent a car beforehand.
You would be able to do so in Interlaken I believe, which isn't a bad option if the price is OK for the one-day, one-way rental and if you are happy to drive on mountain roads for the views (Sustenpass + Oberalp pass is a more scenic route than going via Luzern).

Agreed. If your tour leaves you in Murren, then pick up your car in Interlaken. There is a Europcar and Hertz there.

Murren to Interlaken, you have two options:
- Schilthornbahn down to Stechelberg. Postbus from Stechelberg to Lauterbrunnen. Train from Lauterbrunnen to Interlaken; or
- Train from Murren BLM to Grutschalp. Cable car from Grutschalp down to Lauterbrunnen.

The scenic route mentioned above would be significantly longer, but if you have the time and don't care to see Luzern on the way, its certainly an option.

Whether travelling by train or car, you'll still have to spend one night in Chur if you want to sit in the panoramic cars (only one departure per day in each direction). Travel by train would be less complicated and you could avoid having to waste time by stopping at the rental agency and more time dropping the car in Chur. IMO, the train journey would be a more relaxing and enjoyable way to make that trip.

If you were thinking of renting a car, an International Driver's Permit may not be required but it would be a good idea to have one - https://www.autoeurope.ca/international-drivers-permit-in-switzerland/ .

Interlaken to Chur: 2 1/2 hours to drive. 4 hours and minimum 3 connections to train (via Bern and Zurich). Car pickup and dropoff both took us max 10 minutes.

I wouldn't decide to drive for time savings alone, because by the time you do the paperwork, take a rest stop, refuel, return the car, the difference between 2.5 hours and 4 hours gets slim. Plus, 2.5 hours assumes driving the not-so-interesting motorway from south of Luzern to Chur. If you do decide to drive, make it a scenic drive!