Don't. Do. This.
Grubhub menus are often incomplete (and we all know the prices are wrong). I just checked a nearby restaurant I often frequent and the items I usually buy are not on the Grubhub menu.
If they don't have a web site and you want to see the menu:
Go to either the Google Maps listing or the Yelp listing.
If Yelp, don't click on the menu if they have one within Yelp.
Instead, click on the photos. You'll almost always find photos of the menu uploaded by Yelp users.
That's true, but rare. If there are no recent photos of the menu, then there's a good chance not many people eat there.
In any case, Grubhub menus are probably more likely to be inaccurate than those photos.
Which actually, is pretty impressive when you think about it. It’s not worthless. Even if not totally accurate, it will give you a rough idea of the most popular dishes!
If you want to pay for delivery (not pickup) with a credit card and the restaurant doesn't have online ordering then you'd read the credit card over the phone. Of course you have to say the words "I'd like to pay with credit," otherwise they'll assume you'll pay cash on delivery. Really standard before online ordering became big.
Some restaurants even have a POS system that when you've used a credit card in the past to pay for a delivery order with the phone number/address combination your using for your current order they'll ask you "would you like to use Visa ending in 1234?"
As an aside I didn't know it was a thing until I overheard my roommate doing it. This was 15 years ago now.
I think a lot of the lashback things like grubhub, uber eats is getting lately is precisely because people have become more tech savvy. The "magic" of the app isn't magic anymore to the current generation of users, and they just don't see the value in it that the previous one did.
My opinion: As it becomes more and more commonplace to have "just enough" technical expertise and the tooling is easy enough to DIY, we're going to see services like grubhub become commodified and open - and they know it, so they're doing everything they can to try to keep as much market share as possible.
Restaurant owners are usually not tech people, nor can many of them afford to hire tech people. To expect all restaurants to pay exorbitant amounts of money setup/ maintain online ordering systems is not realistic.
Also, I have never had a restaurant ask me for a card over the phone. Order times are a rough guess based on current traffic, no matter over the phone or an app. And 9 times out of 10 the server repeats your order before hanging up. If they don’t, it is easy to ask them to.
To be fair, I have been surprised many times how difficult it can be to find an online menu for places I like in my area. Lots of places might not even have a website, but in these cases, I actually use GrubHub and the like to read the menus only. I never order through them.
Here is an easy way to beat these broken GrubHub shenanigans. Find an online menu, or use GrubHub only to read the menu menu if need be. Find the real phone number on Google maps. Place your order over the phone. Pick it up yourself and save tons of money on fees (and now apparently save the restaurant from getting screwed too). Make sure to pick up a paper menu on your way out for next time :)