Hi mariolspeter
I've tested the chat on an iPhone and wasnt able to replicate the issue as it appeared to have displayed ok my side.
Did you experience this on a specific mobile device? Is there any chance you could send me screenshots of what you are experiencing? If you could send us a mail via our contact form, we will reply and you can mail the screenshots to us.
http://wp-livechat.com/contact-us/
Kind Regards,
Jarryd