Automatic assessment of wounds using smartphones can facilitate the tracking of healing progress outside the clinic. Prior work proposed SS-PMG-EfficientNets, a state-of-the-art, multi-scale, convolutional neural network architecture for accurate wound assessment. However, the model was previously only trained and evaluated on high-quality wound images captured in controlled environments. This study systematically evaluated the effects of low-quality images on SS-PMG-EfficientNets, finding that the model's performance and consistency are reduced when input wound images are blurry or captured in adverse lighting (too bright or too dark), two factors previously identified as the most prevalent issues in crowdsourced images. Specifically, SS-PMG-EfficientNet was first trained on three high-quality wound datasets containing images labeled with Photographic Wound Assessment Tool (PWAT) wound healing scores, stages of pressure injury wounds, and wound types, respectively. The model was then evaluated on a test wound dataset that was augmented with real-world image luminance, blur, and image compression effects and found that wound assessment accuracy decreased by up to 27%. To improve model performance, we propose a method for instant image quality assessment on the smartphone, enabling low-quality wound images to be rejected immediately after image capture so that the nurse or patient can be prompted to recapture the image. Our evaluation of the proposed image quality assessment and rejection method showed that it increases average accuracy from 73 % to 87%.