

Salt gets into rivers when material that can’t be dissolved is stripped away by erosion. This exposes new water soluble compounds to the water, where they dissolve into the water and are taken to the ocean.
Over millions of years erosion removes innumerable tons of material, essentially mining the subsurface soluble compounds and delivering them to the ocean. Once there, as you mention ,those salts remain in the ocean. On Earth, this process began billions of years ago and has been adding salt to the oceans ever since.
You can observe this happening in many rivers today. The Colorado River is a great one. If you measure is salinity at the headwaters (or heck, probably even the inlet of Lake Powell), and where it enters the Gulf of Mexico, you will observe an incredible increase in salt. There was an international treaty formed around the US delivering river water that is not too salty to grow crops in to Mexico. The US solved that problem by installing a desalination plant on the river!
However without that land based salt mining process, how salty would the oceans be? Lots of good clues in this thread, but I don’t think anyone has offered a definitive answer.
Looking past the caption, I think it’s way funnier when you realize the cat doesn’t actually know how to read. He thinks these are huge cans of cat food.