While Sergey's solution will work fine for the specific example you show, I suspect it will cause problems latter on. The data fragment you have posted looks like basic CSV, (or comma separated values) data, and if so, then the use of quoted strings is deliberate: it is there so that commas can be included in string entries:
"abc", "def,ghi", "jkl"
Is three entries, not four:
abc
def,ghi
jkl
While you could use Sergeys solution, (or just use string.Replace("\"", "") to remove them all first) I would recommend that you use a CSV aware processor instead.
There are a number of ways to help you do just that:
A Fast CSV Reader[
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C# - CSV Import Export[
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Reading and Writing CSV Files in C#[
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