Maybe you could use SS-screws too but my guess is they would not agree with the brass strips.
There is a useful article on this topic at:-
A table headed “Fasteners for Fittings” just over half-way down the page confirms that SS fasteners should be avoided for brass fittings. The reason is clear from the “Galvanic Chart” higher up the page, and the accompanying text. Use brass or bronze fixings for brass, is the message.