We do these all the time. Banners, golf tournament signs... etc. Probably hundreds a year -
You can try to find better quality logos - They are out there... But you could be spending hours and hours getting better quality on some banners / promotional items that will be up for a day and then thrown away.
We usually quality check - Tell the customer "These ones are low quality and dont look good - Let us know if you have better resolution ones, or want us to proceed" Sometimes they get them...sometimes they say not to worry about it and print it as is.
I'd say let the customer know what looks bad - Ask them to contact the vendors for higher resolution logos - If its for an upcoming event, they already have a contact at the company thats sponsoring them, and the company can then decide if the logo is good enough, or get their department on finding and supplying better quality.
Customer supplied artwork is kind of tricky... You can only try your best, but if you go down the rabbit hole of finding 35 different vector logos, your quick sponsor job just turned into a week long hunt.