I'm pretty sure it's "Minä ja Lucky - Tämä on [otettu] meijän hausissa", which translates to "Me and Lucky - this was taken at our house". "Meijän" is a dialectical form of "meidän" (our) and "hausissa" is an American Finnish expression for house.
It's also often called "Finglish" or "Fingliska" since it's a sort of mish-mash between Finnish and English vocabulary and grammar. I think it was quite common among Finnish immigrants around the time that photo would've been taken, but has faded out of use since then.