People today are always rushing and then ruining good meals with careless mistakes, just like back in my mother's kitchen when things were simpler and we actually checked our tools before opening bottles. To fix this mess safely without ruining the evening, you need to take a clean cloth handkerchief or a fine mesh strainer and carefully decant the wine through it into a glass pitcher.
Solving this properly is important to me because swallowing bits of crumbly, degraded cork completely ruins the natural flavor and texture of a good meal, which defeats the whole purpose of gathering around the dinner table together. Take your time, do it right, and it will be fine.