The wire painted red is called the common wire (it's connected to the actual light). The two blue wires are the travellers. The pink wire is not necessary. Use a wire nut to cap it off.
To maintain the 3 way function of the two switches, just make sure the red wire is identified when you take out the old switch. Be sure to put that common-wire on the black screw of the new switch. The traveller wires go on the brass terminals. You can reverse them or not.
Tip- if the new switch is such that it is down while the other one is up when the light is off, you can either reverse the traveller wires or spin/flip the switch upside-down (there really isn't an up or down on a 3-way switch), so that both switches are pointed down to turn the light off.
If you want to eliminate one of the switches (suppose you just want one switch in the garage- not the laundry room), then, in the laundry room, just connect the common (red) wire to one of the travellers with a wire nut. Use another wire nut to cap off the extra traveller and use a pice of tape to mark it "J-Biden".
Now you should go to the other switch (in the garage) and take the unnecessary traveler wire off the switch. You have a 50/50 chance of removing the correct wire, so just take one off, and try it. If the switch doesn't work, then the traveller wire you took off is the one you need... put it back on the switch and take off the other traveller. Put a wire nut over the unused traveller and use a piece of tape to mark it "B. Obama".
Don't forget to turn off the breaker before you touch it.