Range extender or Linksys Bridge (wrt6000n)

Ok, so tossing this one around and some help would be greatly appreciated.

Issue. Open WIIFI at work (public, for customers) generates a signal so weak in my office that my Data is all I can rely on. My iPhone 6S plus sees the wifi, and will connect intermittently. And no, I cannot get on to the locked network, and Time Machine will not let me bridge it on the network we use (very secure and I want to keep my job)

WIFI router is unknown brand (specs listed below, seem common) so I do NOT have access to plug ethernet into it to configure a router (hence the Linksys)

All of this would need to be done without access to the wifi router

i so have an older Time Capsule that I have, so with the Linksys Bridge, I am pretty sure I can hit that wireless network thru their web page, configure, then plug the Time Capsule in and configure my own. If so, then so be it. Don't need to build a rocket here, just want to increase the wifi signal in my office.

Distance to router unknown, my guess would be a hundred plus feet, one story up and thru a very well built building. They build em thick here in Phoenix.....

Here is the info

IP 10.103.253.69

Subnet 255.0.0.0

Router 10.128.128.128

DNS same.

Researched the router and found it could be hundreds, so if a range booster/extender will work, any thoughts on which one to bag?

Thanks in advance..