Holly, you are very welcome!* I'm glad I could id that for you.* Now, the first thing I will say is there are NO dumb questions when it comes to gardening.* :)* You are correct, mallow is the common name of many different genera of plants.* Hollyhocks are referred to as mallow as well as... well, this will explain it better.
As to the one you have found in your garden, I would say to bid it farewell and plant something a little more garden friendly if you like the look of the leaves.* I've always heard that a plant is considered a weed only when it's growing where it isn't wanted.* There is another plant with similarly shaped leaves and plant habit.* One of the nice things about this plant is that water will bead up on the leaves and sparkle in the sunlight.* It's called Alchemilla mollis aka Lady's mantle.* It can seed around the garden if it likes the growing conditions, but if you remove the spent flower heads, that won't be a problem.* Be sure to click on the pictures at the bottom of the page.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.