Site pages are stored in the Site Pages library by default. Since this library automatically inherits its permissions from the site, anyone with read/write access to the site also has read/write access to all site pages. Users with read/write access will see the Edit link shown below whenever they navigate to a site page.

So how do you grant your users Contribute (aka read/write) access to your site and ensure they don’t get an Edit link on site pages? You change the permissions for your Site Pages library. If you grant users Contribute access to your site but read-only permissions to your Site Pages library, they will be able to view all your site pages but not edit them.
Here are the steps to modify the permissions for your Site Pages library:
- Go to your site.
- Click on Gear > Site contents.
- Find and click on your Site Pages library.
- Click on the Library tab and then click on the Library Settings button.
- Click on the Permissions for this document library link.
- Click on the Stop Inheriting Permissions button on the page’s toolbar.
- Say OK to confirm you want to customize the permissions for this library.
- Modify the library’s permissions as desired.
TIP: Make sure you give users read access to your Site Pages library. This will ensure they can see and access your site’s home page.
Source: https://blog.splibrarian.com/2014/04/20/disable-edit-link/