What did you match from? As far as the public offers go, Delta only does what they call "Status Match Challenges" - which are just challenges.

If you matched from United Silver (as in your profile), the highest you can go is Delta Silver.

If you got a higher offer, but only met the lower Silver requirements, you would retain the higher status for 90 days, at which point you fail the challenge, but you keep the status for a challenge that you met, up to the challenge status - so you'd keep Silver.