Hi Lisa, for your return trip, you will need to purchase a Strasbourg —Paris ticket from SNCF Connect (or Trainline if you prefer, either one is fine).
To get to the station at Saint-Remy-les-Chevreuse, you should go from Gare de l’Est to the RER B (you can either walk from Gare de l’Est to the Gare du Nord to catch the RER B, or take Metro line 4 from Gare de l’Est one stop to Gare du Nord.). You will need to go to one of the Ile de France/ RER train ticket machines upon your arrival to buy a special RER ticket to your destination.
At Gare du Nord, you would take the RER B (suburban train) to Saint-Remy-les-Chevreuse (luckily it’s the end of the line, so it’s easy to know which train to take, the correct ones will be labeled/advertised as going to St-Remy-les-Chevreuse). This will take around 50 minutes if the train is running on time. Notice !! Be sure to keep the ticket you bought at Gare de l’Est, as you will also need it to exit the station at St-Remy!
Another option would be to take the train from Strasbourg back to CDG airport (instead of Paris proper) and take the RER B directly from there. It would be a longer ride, but would keep you from having to switch from Gare de l’Est to Gare du Nord.
For a little help on how you buy the RER ticket at a machine, please see this video from Les Frenchies (they are focused more on local Paris tickets, but the same machines will sell you the ticket you want. Pay attention to what they show you about which machine to use. Keep in mind you can not use a Navigo Easy to buy the ticket you want to St-Remy-les-Chevreuse).
https://youtu.be/_aHzrKnutAU?si=xpPHgQKtsCAgkYBE
At 2:30 of the video, he shows how to understand which machines are the right ones for buying your tickets.
At 4:14 of the video, she shows you how to buy a single ticket within Paris. Pause the video at 4:20 - you can see that she chooses a t+ ticket, but you want to choose « Tickets Paris Region” - on the net screen, you will type in Saint-Remy-les-Chevreuse . . . . Also try typing St-Remy, I don’t know which it is.
The machine will issue you a paper ticket like she gets (video at 4:52) and you put it in the turnstile like she shows. But please note !! On the RER, you must also put your ticket in the machine when you EXIT the system — so keep your ticket so you can get out of the station at St-Remy-les-Chevreuse!