In my case, there are stories that go with images and when they are reposted, the stories get missed. My kids love to get messages/feedback on the cosplays they do and when things are reposted, they miss it. But in general, when it comes to images of minors, always ask the poster first before copying and rebroadcasting on the internet. There are reasons why I don’t post to certain sites, mainly because they have rules that when items are posted, they become property of those sites.
Also, you may remove your initial post on tumblr, but all the reblogs will remain, unless tumblr support is contacted so that all those reblogs can be removed. So it’s not as simple as saying ‘oh, if you don’t want this I’ll take it down’