The committee will be interested in what the letter tells them about you, not whether it has a signature in ink.
People submit LORs without signatures all the time. A PDF with an original signature requires a printer, a pen and a scanner, which not everyone has or has time for. (Yes, you can also paste in a scanned image of your signature, but where do you get that without a pen and a scanner?)
I suppose the lack of a signature might affect some people's overall impressions of a letter, including how much effort the author seems to have put into it, but we've been living in an electronic age for quite a while now. Unless they have some reason to doubt the authenticity or perhaps an unusual policy requirement at that institution, I think most committees will ignore the lack of an actual signature and focus on the content. It won't affect their decision.
The reason universities want signatures from students but not so much on LORs is to create some enforceable contractual conditions and because of the conflict of interest that exists when students are asked to self-report that doesn't exist with references. Asking for a signature reminds the students of the seriousness of the situation, that they are on their honor to submit only correct information, only their own personal essays, etc. When you ask for a signature, you get better behavior.