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'Your clothes will get dirty.' 'No problem. They're not that clean to begin with.'

Literal

'Clothes get-dirty [probably-でしょ]' 'That [topic-は] no-problem. Originally not-very clean [isn't-じゃない][and besides-し]'

ノープロブレム is a loanword from English 'no problem,' used casually. もともと 'originally, to begin with' sets up the punchline — the clothes were already dirty. し at the end gives a trailing, casual reason: 'besides, it's not like they were clean anyway.' A humorous, self-deprecating exchange.