First of all, that rate seems "too good to be true" given current 30-year rates, which are near or over 8%... It seems like either a "teaser" promotion that will end up being a much higher than advertised rate, or a variable rate, or some other catch.
Even so, a 0.1% drop in interest rate is probably not worth the cost of refinancing. For a 480k loan it amount to $40 per month "savings" in terms of paying less interest. But you're already paying more than the monthly payment, so over 5 years it just means that you'll owe about $2,000 less than what you would with the current loan. If the closing costs are back-end loaded somehow, it's probably at best a wash.
The general rule of thumb is that refinancing only makes sense if it drops the interest rate by 1%, depending on how long you plan to be in the home (the longer you plan to keep the loan, the lower the rate drop can be to break even).
Looking at the image you added , your closing costs are $15,000, which almost certainly includes about 5 "points" which is another term for prepaid interest. You're paying extra at closing in exchange for a lower interest rate (which is almost certainly not a great deal for you)
This sounds like a very shady way to make someone think they're getting a great mortgage.
In short, they're asking you to pay $15,000 now to save $100 a month - which would take you over 12 years to break even.
Based on your additional info it sounds like they made a mistake with the original loan, and now they are not able to sell it and get it off their books (why they want to do that is a longer discussion). Now they want to redo your loan at roughly the same rate and get all of the documents right this time.
The bottom line is if they are offering a new mortgage at basically the same rate with no additional cost, then yes it's worth it. Even if it's minimal cost to you, the most basic calculation is to divide by the total cost to you by the reduction in the monthly payment - that will tell you how long it will take to make up the extra cost. They may be willing to eat the cost in order to get the loan off of their books.