I'm currently approved with Pulte mortgage which is Centex preferred lender . I'm closing December 7

I'm getting $1000 towards closing for using them plus Pulte is waiving the 1% originating fee.

When I talk to them about looking my rate, they say it will be 3.5% , . 30yr FHA

Should I talk to another lender and see if they match and lower the above .?

How can I get Pulte to lower their fees and rate.

My middle score is 680 as reported by Pulte.