In the Middle East, a guest is greeted with a sprinkling of rosewater on his/her hands as a sign of welcome.
The sprinkler is filled with rosewater to the top of the lower container. The sprinkler is then turned upside down and held in the right hand with the "bulb" resting in the palm of the hand and the long neck pointing downwards, between the middle and ring fingers. The sprinkler is then shaken and drops of rosewater come out of the top. ( Hope that makes sense )
Don't think it is a bat, more like a way to enclose the writing.
best wishes, a40ty