Green’s Dictionary of Slang

hoot n.2

[? fig. use of SE hoot, an abrupt, sharp cry]
[late 19C+]

1. (orig. US, also two hoots) a very small amount; anything or anyone considered unimportant, insignificant.

2. (US) a euph. for hell.

In phrases

give a hoot (v.) (also ...two hoots, ...a hoot in hell, care a hoot, ...two hoots)

[mid-19C+] to care; usu. in negative use, e.g. who gives a hoot?