Like always it should be a vector file
Yes, and placing a PSD in Illustrator and saving as EPS or AI doesn't magically turn it into vectors. Neither does saving it as a Photoshop EPS.
If their logo can't be reproduced in one color, it isn't a logo.
I know you didn't design it, but whoever did design it should have delivered a complete package of vector graphics that includes a single color version, along with whatever multi-color versions they wanted, and then perhaps, (but not as a rule), one or more stylized versions with raster-only effects like blurs, shadows, shading, etc. If all they got was an effect-laden raster image, they got taken. And now they'll have to pay again to have someone, (you?), recreate a flat version in vectors as should have been done in the first place.
If you're preparing the graphic for output by a provider who requires vectors, forget the pillow emboss.