If I try to share a link without a photo it seems not to work switching it off when saving. The preview seems to work, after saving the link the photo is visible again.
It seems like that is bug, can you try download my attachment file (extract it) and replace into this file location : JoomlaFolder/components/com_easysocial/themes/wireframe/streams/links/preview.php
I will report this to our developer regarding this and include a proper fix in next release version.
I have a little bit lost here, do you mean when you share a link but this link do not have contain any photo and it work fine from the preview but it still show some of the photo on the stream?
If yes, perhaps you can share with us which link you share? So we can better have a check.
Please check the two last activity entries on my page. Those two are links which I wanted to share without the photo - I switched off the photo.
Feel free to try and delete afterwards.