I've never used Laravel Tinker and have no interest in using it, so let's see if it's possible to remove the laravel/tinker package which comes with Laravel by default.

It's probably wise to clear the cache and config prior to removing the package:

php artisan cache:clear  
php artisan config:clear 

Then remove the laravel/tinker package with composer:

composer remove laravel/tinker

./composer.json has been updated
Running composer update laravel/tinker
Loading composer repositories with package information
Updating dependencies
Lock file operations: 0 installs, 0 updates, 2 removals
- Removing laravel/tinker (v2.6.2)
- Removing psy/psysh (v0.10.9)
Writing lock file
Installing dependencies from lock file (including require-dev)
Package operations: 0 installs, 0 updates, 2 removals
- Removing psy/psysh (v0.10.9)
- Removing laravel/tinker (v2.6.2)
Generating optimized autoload files

If your version of Laravel predates the package discovery you'll have to remove it from the file in which it's registered. And obviously remove any instances where the package was used throughout the codebase (not sure if that needs to be done with Tinker, we'll see if something breaks unexpectedly in the future).