To delete photos from the app, tap on the image and then click Remove (located in the bottom left corner).

On the web, when you click on the photo icon from your user history or from the homepage at foursquare.com, you’ll see a larger version of your photo.  Click the Delete button on the bottom right (the Delete button will show when you mouse over the image). When the pop up asks if you want to delete the photo, select OK.