"developed by" issues

Hey guys,

long time no see - hope everyone’s been keeping well!

I’m having a small issue with a company I’ve been working with. They’ve essentially outsourced me to do a website for them, because they can only do design. At the bottom of the website, I’ve put “Designed by their design company - Developed by my company”

They’ve asked me to remove the link to my website as it’s “their” project. Should I do this, or should I hold out and put my foot down?

Thanks in advance!