No apologies necessary. In fact my apologies to you for completely missing the "pencil" reference and the picture reference. My brain was already in the act of formulating a response to the original post and my assumption was that you were referring to the cache notes a little further down the cache page on the website. I find it difficult at the best of times to think and read or think and speak as it is. Throw in trying to type or write it and it gets even more difficult for me. I have a tendency to think much faster than I speak or write. More aptly put, I speak and write much slower than I think. I am not always a good multi-tasker. I don't often comment in the forums for that reason.
As I mentioned, I have not gone after very many mysteries. The ones That I have gotten were with my cousin (blind in one eye) who had already done the work for the coordinates and then I helped by providing an extra set of eyes at GZ. So thank you for your information as I had never noticed the "pencil" next to the coordinates on a mystery cache page.
As to whether you are using an Android, Apple, or whatever device, no need for apology there either. Personal preferences are exactly that. I use the official app on my iPhone because that is what I have and works best for me at the moment. Personally, I would not mind using Android or Windows Phone and the best app on either of those if that was what worked best at the time. I am a tech nut according to my wife but I don't subscribe to a single branding. I use a windows laptop, Android tablet and the iPhone on a daily basis. All are a means to an end for me.Nevertheless, if you have an Android (sorry apple folks) your phone uses the new coordinates you replaced on the listing page. As far as your phone is concerned the coordinates your manually entered on the listing page are the "real coordinates". This is why I do not use the official geocaching app. I purchased it but it just is not up to par with two other apps that are on the market. This is obviously my personal opinion and my comments can be stricken if need be.
It is so much easier to update the coordinates on the listing page and let you phone app calculate the shift than trying to manually enter the new coordinates in the phone, while in the field, then proceed to the cache. All I have to do is start the app and I'm off. Otherwise, you have to pull up the coordinates, copy and paste them (which doesn't always work because you have to enter north and west separately so you end up writing on your hand), then you can finally get going. That is a hassle.
Sorry for the rambling. My main point is updating the coordinates on the listing page is the "way to go". If you own an iPhone you get to do it the hard way. Sorry. Having said that, anything is easier than how I did things back in 2005 so it is all relative. I'm spoiled with Android technology and c:geo.
I did do a test now that I know about the "pencil" on the cache page and the official app on the iPhone does indeed update the navigation page with the corrected coordinates as you described. It seems that updating the cache page via the website or as I describe via the app navigation page will accomplish the task.
Thank you for the information and the conversation! Hopefully we have helped each other (you helped me develop a new wrinkle on my brain) or help someone else who might be watching this thread or happen on to it in the future.
Happy Caching Y'all!!!!