I would like to use a screenshot of Google Maps on my company's website. But I'm not sure they allow using the maps besides through their API. Maybe it's OK if the image points to the Google website?
It isn't allowed. You have to use the Google Maps API or ask for a High Res Screenshot directly to Google.com
You can use a Google Maps image if you give attribution in the way they want it.
Found on Permissions - Google
Using Google Maps, Google Earth and Street View
All uses of the Content must provide attribution to both Google and our data providers. We require clear, visible attribution when the Content is shown. You may not move the attribution to the end credits or fade it out after a few seconds.
Note that if you embed a classic map, Street View panorama or My Map; use one of our APIs on the web or in an application; or export a video or JPEG from Google Earth Pro, the necessary attribution is already baked into the map and no further credit is needed. Learn more about how to properly credit, as well as how to identify providers, on our attribution guidelines page
If you are unwilling to meet our attribution requirements, contact our data provider(s) directly to inquire about purchasing the rights to use the Content directly. You’ll find provider contact information listed on their websites.
You can use a screenshot if you include attribution visible to the average reader. The attribution must be in conjunction with the screenshot, not at the bottom of the page. See https://www.google.com/permissions/geoguidelines/attr-guide.html