It shouldn't hurt the grass assuming the herbicide you're using is compatible with your type of turf and you spray at the right rate, and during the right temperature windows. Triclopyr is great on violets too. Triclopyr is fine for tall fescues and bluegrass. It's probably fine on rye grass too, but honestly I don't remember without looking at the label.
I like using a surfactant in your tank mix but once again "read the label". Any Ace Hardware should have a surfactant. It's normally about $8 for a small bottle but it really helps make the spray more effective at killing weeds. Surfactant in this case is basically just a soap to break water tension which will create find drops on the weeds. Bigger drops aren't as effective as they tend to join up into globs of liquid and then flow off the leaf surface. Finer drops stick and the plant absorbs the herbicide better.
I would advise against most homeowners combining triclopyr and other herbicides like 2,4-D in the same tank mix. It's possible, but introduces greater chances of turf injury for those not versed in herbicide use. In other words, don't home brew your own weed killer.