Google doesn't allow any logos or text on a product image. They call it a "promotional overlay." Most of the time when a logo is added to a shopping image, we get disapproved for "promotional overlay." Even though that is not the case, Google will still flag it as such. We add the logo to the responsive ad for shopping, but sometimes there is not enough room to display it depending on what digital property your seeing the ad.
If a promotional overlay is detected on a main image, that product will be disapproved because it doesn’t meet the image requirements. Here is their article all about this.. Google automatically detects any logos or words and automatically disapproves it.
The Smart Shopping campaign has a remarketing aspect to it. This means it will follow recent website visitors around the web and show the product that they looked at. These ads can often appear simple with very little text, however Google's algorithms have determined that this is the best way to remind interested leads to come back and complete their purchase. These are dynamic (which means that Google's algorithms decide whether to show a logo, what text to include, etc. based on the person they are showing the ad to and the space they have available).