If each affiliate has a variety of subIDs you need to track (e.g., to identify various sites/campaigns where they've posted their affiliate link), they could add a custom parameter to each of their link URLs as explained previously, which would then be passed thru to your landing page URL.
Then custom scripting in your page could look for the value of that parameter in its URL and dynamically append that value to a &custom= parameter on all of your cart button URLs in your page -- e.g., https://www.e-junkie.com/ecom/gb.php?c=cart&i=XXXXXX&cl=173371&ejc=2&custom=SubIDGoesHere -- so clicking any cart button would pass that value to the cart as a custom parameter for the order.
If you need that custom value to be carried from page to page on your site, so all of your cart button URLs site-wide could have the &custom= value appended, your scripting might set a cookie for the custom value, and then it would read that cookie to get the value to append to the &custom= parameter in your site's cart button URLs.
BTW note that, although this custom value is passed to the cart by clicking an Add to Cart button, the custom value itself is only associated with the whole order, rather than any particular item in the order, so there could be only one custom value per order no matter how many items are ordered. Appending it to every cart button's URL just ensures that the custom value will be passed to the cart no matter which button(s) the buyer clicks.
That custom value would appear in your Transaction Log and can also be inserted in your thank-you pages using the [%custom%] template variable in your Common Thank-you Page HTML field, which would insert the order's custom value when the page is generated. This could even be used to insert that custom value within tracking code in your thank-you page, as the substitution is performed before the page is sent to the buyer's browser. If you have set up our Integration feature to POST order data back to a script URL at your end after checkout, the custom value would be included in those submissions as well.
The custom scripting in your site that I described above is something that would need to be programmed from scratch by an experienced Web developer, who would fully understand everything I've described here and recognize exactly how to implement it. This is not something that can be accomplished with settings in WordPress nor any ready-made WP plugin. Please contact developers in the directory I linked previously for help setting this up.