If your raised bed is filled with a very fast draining medium, you are probably ok. Perhaps dig one plant and see if the roots look good and healthy, if so let it be. Pulling the straw won't hurt anything except to disturb the plants. They look real nice in the picture. One of the reasons we used raised beds for garlic is to protect against excess moisture at this time of the year. If the bed drains fast enough so that there is not water standing in the beds, and especially if your walkways drain quickly as well, you should be fine.