Some times there are aspects of local produce that are worse than what you could find at the grocery store, and celery has a couple of those. Increased exposure to sunlight causes celery to develop more chlorophyll (the green color) and more lignin (what makes it tough), but whether its due to variety, conditions, or techniques, we couldn’t tell you why local celery doesn’t have the bulky greenish-white stalks of the grocery store version. The consequences are that this celery is small, tough, and bitter, but intensely aromatic.
Some ways to deal with this is to use the celery for stock, where it would be strained off anyway. Or you could chop it small reducing the tough long strings into small pieces. Or the most “french” thing (a term we use to refer to a task that’s overly laborious in the pursuit of perfection) would be to peel the celery to remove the strings entirely.