A few basic questions are in order, like what fab code are you working to, what does your WPS say (assuming you have one), etc.  "Normal" selection would be 316LSi.  Why would any other filler be considered?

What you are asking is a quesiton that pertains to alloy service design. When welding 316 unless you have service design info to the contrary then a 316 would be the first choice (somteimes you can even go the other way using 308). Since 317 is a higher alloyed version of 316 the choice would most likely not be problematic but neither would it be cost effective.
It is not unusual for a fabricator to not have knowledge of a particular service, and though helpful it is not necessarily incumbant upon them to do so. Design info should come from the customer. You should have a specification that essentially answers this question for you.

for the record the difference between 316L and 317L is approximately an additional of 1-2% chrome, nickel and Moly
As Js55 mentioned this would be a case of overmatching filler material.  Under D1.6 316L to 317L is considered weldable although the reccommended filler material remains 316L.  Using 317L for 316L would be similar to using 308L stainless steel for 304L  it's a case of overalloyed filler material.

Perhaps the over alloyed filler material has been specified to  maintain desired alloy content in the weld zone? or to achieve a specific grain structure or ferrite content. Without knowing the service conditions that would be a hard question to answer or even to determine if such a filler was neccessary.

If you have access D1.6 - Stainless steel welding code. has tables with filler selection for all the common grades of stainless that's where I got my information above.  Personally I can't think of the precedent to use an over alloyed filler on 316L but I don't think it would hurt. merely be more expensive.