One variant using sed:
for file in *tif; do newname=$(echo "$file" | sed 's/_//;s/\.\([0-9]\)/\1/g'); mv -v "$file" "$newname"; done
'Sep04_17.00.37.tif' -> 'Sep04170037.tif'
'Sep04_17.02.02.tif' -> 'Sep04170202.tif'
'Sep04_17.05.54.tif' -> 'Sep04170554.tif'
'Sep04_17.07.17.tif' -> 'Sep04170717.tif'
'Sep04_17.08.41.tif' -> 'Sep04170841.tif'
Using mv -v in the example only to show before/after. YMMV.