Thank you for your question. Before I answer I could use a little more information.
   Are these the stems from the previous year? I take it they haven't bloomed this year.

 It appears that these are the dead stems from the previous year. If so remove them with no problem.

  There is a fungal pathogen that affects Shasta Daisies but I am reluctant to say this is the problem. For now, it would appear this is just leftover debris from last year and can be removed.

 Thank you again.

   Just checking in again to see if your question was answered satisfactory or if you require additional information.

Happy gardening.