This is a dinky toy Dlink.. and I am not sure it is really suitable.
Anyway.. first thing to do is download the manual.
ftp://ftp2.dlink.com/PRODUCTS/DIR-822-US/REVC/DIR-822-US_REVC_MANUAL_063017_v3.01_US.pdf
You cannot extend wirelessly so it must be setup as roaming network.. that means the Dlink is bridged.. ie no router function.. and it must be set to create a wireless network same as your TC.. however TC wireless name must comply with SMB standards not Apple..
ie if your apple wireless name has spaces and an apostrophe please fix it to be short, no spaces and pure alphanumerics.. password is the same rules but longer.
First problem is the D-Link makes no reference to WAP (wireless Access Point) mode in the manual and the only setup option appears to be as full router.. that being the case you will have to set it up in WAN BYPASS..
This is a bit more complicated.. Let me give you an example rather than try to explain it from scratch..
Get the IP range your TC is using.. by default it will be 10.0.1.1 assuming you are running it as a router. Or it will likely be 192.168.x.x if the Arris is your main router and the TC is correctly bridged to it.. please do open your airport utility and click on the TC to get its IP address.. I will operate on Arris being 192.168.1.1 and the TC is using 192.168.1.10 .. plug your own values in ..
So you will need to plug the DIR-822 into the TC or the Arris .. by ethernet.. but not yet..
First of all plug your computer into DIR-822 by ethernet and reset it to factory to clean up any mess that you have made.
Home IP of the D-Link is 192.168.0.1 so type that into your browser and put in the username and password.. usually admin and blank by default but check the base.. you probably have already got this far.
Go to manual setup.. the wizard here is useless.
Go to the network tab.. p50 in the manual I linked.
Set the LAN IP to identical range to the TC but different last number.. eg.. TC is 192.168.1.10 I used in example.. make the D-Link 192.168.1.254 (the last IP in the range).. you can make sure nothing already has that IP but it should be safe.
Don't just follow the example.. put your own IP in.. if you need help give me the screenshot of the TC so I can see its IP.

Secondly turn off DHCP server.. it is not going to work as the DHCP for the network as you already have a router.
Apply those settings.
Your computer will now lose connection with the Dlink.. this is expected..
Connect LAN port 1 of the Dlink to your TC or ARRIS LAN port. NOTE.. NOT WAN.. you are not routing so don't use WAN..
Plug the computer into LAN port2 etc.. and in the browser go to the D-Link address you just created.. in my example 192.168.1.254 (write this down as you will need to remember it.. on a label on the base of the dlink is good way plus all the passwords).
Now go to the wireless configuration and set the SSID the same as you set the TC wireless name.. and the same password.
Apply the settings..
And you are done.
Your Dinky Toy Dlinky is now working as a WAP instead of as a router.