The online designer will check the image based on 300dpi at the print size, which is the recommended file resolution. For e.g. if you have exported your file at 300dpi but the print size is 3 inches width and you enlarged to 10 inches, this is effectively reducing the dpi from 300 to 90.
If this sounds foreign to you or you are not sure how to check, then an easy way to check if the image quality is acceptable to you is to open the image on a computer (such as Photos on Windows or Preview on Mac OS) and enlarge it to the approximate print size.
Firstly, make sure you trim/crop off all the transparent pixels around the design. Then, if you are looking to print at 10 inches width, enlarge your file (you can use a ruler on your screen for best result) and see if it's blurry.
If it looks good to you, then you can accept the warning message. But if it's pixelated or blurry and it's unacceptable to you, then do not proceed.