Trawling or scraping the data is a poor practice.
If there's a relationship whereby the site trusts you with having up-to-date stock info, then there are various ways for them to share the data with you.
What I wrote earlier was intentionally very generic. I said "have your script go out and get the data" ... that "go out and get" could be in various forms (direct database access, a REST query, a CSV file produced by their end and stuffed into a URL that your script can read, etc).
torvista suggested one approach ... have them set up a timed script on their end to export a CSV file of product ids and inventory counts. Then have your script read and process that info.
If they will write a script that extracts the data and puts the CSV file into a folder on their server (a folder not advertised to anyone but you, and maybe security-restricted to only the IP address of your webserver), then your script could check to see whether the file exists, and process it.
I also wrote generically in how to process the script, mentioning that it should only apply updates where a change is needed. ie: if there is no info for a particular product ID, skip it. And if the quantity they say they have matches what you have, then skip it. This minimizes the amount of changes pushed into your database, thus minimizing performance problems.
Of course if you're asking for more info than just product ID and available stock for that ID, then things get more complicated.
But there are lots of ways to tackle your situation as you described it.
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