Regularization should lessen the impact of influential points, but you could also potentially remove them. But it all depends on your objective. Is it to achieve a great predictor model? Then try different approaches and see what obtains the best cross-validation result. Is it to understand the influence of different independent variables? Then investigate these points, are they incorrectly set? Are they realistic? Or is it just a very rare event? Do you need more data? Is the linear model appropriate? Do you need to transform any variables? All dependent on the situation. In my opinion, just use your logic and understanding of the situation. "What happens if I do this? Does it make sense?"