Most of us want our daisies to have beautiful flowers on them. It's the entire reason we planted them in the first place. So when they look like this your first instinct might be to pull them up and toss them. Especially here in Texas they don't do so well. They come from South Africa where the climate is quite milder. Temperatures here can get over 110 sometimes whereas their native land tops out in the mid 90's. Sure it freezes there sometimes but they don't mind that so much. What you don't see is the new flower forming inside there that is due to bloom in a day or two now and the wonderful new plants that you can have by planting the seeds from these flower heads.
The seeds are relatively easy to start. After the flower head has dried up for a week or so just remove it and either remove the seeds yourself or let them dry some more until they fall out. Plant the seeds on the surface of moist soil in temperatures you wouldn't mind living in yourself which makes a kitchen counter perfect for this. Cover the pot with plactic wrap making sure you have some space between it and the soil and let it germinate. once you see them sprouting remive the plastic and let them grow in a greenhouse or under grow lights. Transplant when they look big enough.
Some people like to keep them in 3-5 inch pots so they will want to bloom while others stick them outside.