There are a couple different reasons why your clients doesn't see this option displayed on their web itinerary:
1. You have shared a Proposal instead of an Itinerary
If you created a Proposal to share with your clients, the option to download the Trip Plans app is not available to access from a Proposal. If you wish for them to view the Proposal in the mobile app, you can copy the Proposal into an Itinerary by following these steps.
2. You have disabled the "Get the App" button for your client's itinerary
To enable the option for your client to download the app, go into the itinerary to edit and press Settings at the top.
Next, scroll towards the middle next to "Client Actions" and check the box associated with "Get the App. This will automatically display the option on the web itinerary for your client.