Depends on the coin and the counterstamp. An interesting historical counterstamp on a common low grade large cent? The counterstamp add value. Someone punching in a non-descript countermark on an XF 1914d? It just lost tons of value.
Yours is a case of a sad coin. I have seen similar. Once a dealer had a very attractive 1914d, (which is why I chose the date earlier), that was a beautiful glossy brown AU. Unfortunately, it was offcenter by about 35%. Now, either one of those things will make a valuable coin, but combine them and overall it hurts the coin. No date collector needing a 1914d wanted such an offcenter coin, and no error collector wanted to pay for a key date. Same with yours. No collector needing the overdate will want it with the countermark, but a countermark collector will not want to pay for the overdate. Some coins make you sad.
I believe they significantly hurt numismatic value, but increase (though it's difficult to gauge by how much) historical collectible value. Edit: To the coin pictured, I think it might actually be a somewhat neutral situation. It's a VG8 without the countermark? FS-301 $85 PCGS guide value would probably sell for $50-$60 on eBay. You sold it for $30 on eBay, so I guess that means it cut the value in half.
Agreed! It's all in the historical significance of the counterstamp and the numismatic value of the coin. Will add value to a common coin in many cases, but rarely to a rare and desirable coin. There are exceptions of course. Bruce