You could use a nested Any() for this check which is available on any Enumerable:

bool hasMatch = myStrings.Any(x => parameters.Any(y => y.source == x));
Faster performing on larger collections would be to project parameters to source and then use Intersect which internally uses a HashSet so instead of O(n^2) for the first approach (the equivalent of two nested loops) you can do the check in O(n) :

bool hasMatch = parameters.Select(x => x.source)
                          .Intersect(myStrings)
                          .Any();