Get a grout removal tool to get it out. Then put new grout in, clean up while wet, and seal.
Bettie: Kathy's answer was perfect!
Dig and scrape out grout. Don't replace will always crack against wood, just caulk carefully . Try to match baseboard or tile.
I would swap grout for silicone caulk for any job I can imagine. Grout starts with sand, which becomes dirt, and dirt dries to dust, and unsealed grout exposes walls and counters to degradation. I’ll choose the chemical-based caulk. What was the old slogan? “Better science for better living”, or something similar.