What to do if one out of 2 one-hot encoding variables have a very high p-value? I ran an OLS model on a dataset with 2 categorical variables. One of them was gender. The other one had 3 different categories. I used one-hot encoding for it during pre-processing before running my model. 

Variables in the image: Embarked_C and Embarked_Q.
The results showed a p-value for Embarked_Q as 0.785. In this case, should I remove both Embarked_Q and C or just Q?
You should keep all of levels as they collectively describe the feature. Removing the insignificant ones will bias your coefficients and distort your interpretation (e.i. change the reference level).  

Here are some stats.exchange references:


Is it advisable to drop certain levels of a categorical variable?
Can I ignore coefficients for non-significant levels of factors in a linear model?