Here is the tour link, however, we did our own backpacking, so n

So not sure of the service as good or bad.

actually it is not strictly backpacking, you have to stay in huts and meals are provided. June might be too cold and covered with snow.

https://www.backroads.com/tours/dolomites-hiking-tours?p=D485_M&utm_source=google&utm_medium=cpc&utm_campaign=Italy_Opt&utm_content=Dolomites_Hiking_Tour&gclid=CjwKCAiAyMHhBRBIEiwAkGN6fBBsIhG8RnnznYPEHVUuoU68QPBl9cCbvIpJnPK3vnREdEZm9CuTeBoCPdQQAvD_BwE