The branch in question should be removed.  Others may need attention too.

Although many trees need little or no pruning, those that do should be attended to regularly before wayward branches get very large.

The following publications discuss linden's growth habit and how to manage it. (Linden trees are excurrent--trained to a central leader.)

http://hort.ufl.edu/woody/good-quality2.shtml

https://cmg.extension.colostate.edu/Gardennotes/614.pdf

We recommend asking a certified arborist to do the pruning. It might be necessary to spread the work over two or three years.

If you decide to hire an arborist, the following information may be useful:

https://extension.umn.edu/planting-and-growing-guides/how-hire-tree-care-professional