Fuel injector cannot and should not damage your fuel pump.
The fuel injector cleaner gets dumped into the gas tank when your gas tank is full or before you fill up your gas tank with gas.
Then the fuel injector cleaner mixes with the gasoline which then helps keep the fuel pump clean as well as the fuel lines, fuel injectors and throttle body clean.
It's recommended to dump a bottle of fuel injector cleaner into the fuel tank every 2 fill ups of gasoline.
Doing that will keep your fuel injectors and fuel lines clean.
Also make sure to change your fuel filter after every 10 years or 50,000 to 100,000 miles to keep your fuel system working properly.