What to do about this plant?
We think this looks like Carolina geranium (Geranium carolinianum) also known as wild geranium or crane's-bill.
It is a biennial, and spends it's first year as a low rosette and overwinters in that form. The plant dies out after making seeds. Reproduction is by seeds, which can germinate in late summer/early autumn or even spring. It tends to grow on dry, low fertility sites.
The least toxic method of control is hand weeding.
In your lawn you can use a broadleaved weed control, and in your garden bed you can carefully apply a non-selective weed killer containing glyphosate (like Round Up), being careful not to contact desireable plants. Follow all label instructions for any herbicide/pesticide.