bash wget a remote URL, then extract the URLs from the anchor tags in that URL

getlinks

get from a remote file to STDOUT:

wget -qO- https://www.membrane-australasia.org/gallery/imstec-2016-adelaide-part-3/ | 
grep -Eoi '<a [^>]+>' | grep -Eo 'href="[^\"]+"' | 
grep -Eo '(http|https)://[a-zA-Z0-9./?=_-]*' |
uniq

get from a remote file to xargs and download each URL

wget -qO- https://www.membrane-australasia.org/gallery/imstec-2016-adelaide-part-1/ | grep -Eoi '<a [^>]+>' | grep -Eo 'href="[^\"]+"' | grep -Eo '(http|https)://[a-zA-Z0-9./?=_-]*' | uniq | xargs -n 1 -P 24 curl -LO

local file version:

grep -Eoi '<a [^>]+>' file.htm | grep -Eo 'href="[^\"]+"' | grep -Eo '(http|https)://[a-zA-Z0-9./?=_-]*' | uniq

Sources
https://unix.stackexchange.com/questions/181254/how-to-use-grep-and-cut-in-script-to-obtain-website-urls-from-an-html-file

According to that link your script is not correct. It might work in 98% cases, but it doesn't mean it can be reliable. Yup, that's it.
I would suggest to use ElementTree from Python or any other XML parser for this. Actually in the shell you may find nice XPath compatible parsers.

Thanks for the info, much appreciated. I'm curious, how did you come across my gist?

Another easy way to get a list of URLs from a page is to use lynx: https://unix.stackexchange.com/a/684704