Some of the Regina like this are two-notch and the Suntour two-notch removal tool will usually work. If someone hasn't removed properly in the past, the notches may be munged up and deformed so the two-not remover won't fit in.

PRO TIP: The biggest mistake newbies make when removing two-notch will make you slap yourself in the face. Secure the freewheel removal tool in place with a QR skewer (nut on tool side) so it doesn't slip. As you see in the Velobase pic above, the edges of these freewheels are often marred from someone NOT securing the remover, which then slips and ... you see the end result.

If I had a choice between lightly filing my remover and lightly filing my freewheel body, I think I'd modify the tool to make it fit... my 2¢ of course!