The following worked for me with QGIS 2.18.11:

1. Add raster layer -> choose the original TIF file
2. Set a CRS -> based on the .prj file which comes with the original TIF file choose EPSG:32613 (WGS 84 / UTM Zone 13 N). Depending on your settings you will be asked to choose a CRS when adding the TIF file as raster later or you will have to right click the layer in the layers panel and select "Set Layer CRS"
3. Right click the layer in the layers panel and "Save As..." -> Format GTiff

The following worked for me with QGIS 2.18.11:

1. Make sure that the original .tif and .tfw files are located in the same folder.
2. Add raster layer -> choose the original TIF file
3. Set a CRS -> based on the .prj file which comes with the original TIF file choose EPSG:32613 (WGS 84 / UTM Zone 13 N). Depending on your settings you will be asked to choose a CRS when adding the TIF file as raster later or you will have to right click the layer in the layers panel and select "Set Layer CRS"
4. Right click the layer in the layers panel and "Save As..." -> Format GTiff