Simplify a logic expression
The point where you arrived is almost right:

$$
C+\overline{A}B\overline{C}=C(1+\overline{A}B)+\overline{A}B\overline{C}=\\=
C+\overline{A}BC+\overline{A}B\overline{C}=C+\overline{A}B(C+\overline{C})=\\=
C+\overline{A}B
$$

That should be the same answer the K-map and whatever reduction software should give you.