Good afternoon Stephanie, thanks for contacting us. Hopefully we can get to the bottom of this and help you and your Linden tree. Do you mind sending me some additional pictures, of the entire tree and one of the some of the black spots close up. A few questions as well...How old is the tree, where is it located in your yard (feel free to send a pic if thats easier), does it get mostly sun, shade, etc. Is it in your grass or in mulch. Do you winter water (if so, how often and how much), where do you live? 
Please feel free to email us back at <personal data hidden>
Thank you,