There's not enough information in your question to say whether they will influence your SEO or not. But my guess is "probably not".
If these are regular 3xx redirects then yes, they will pass rank.
However, if the redirect URL/script is blocked with
robots.txt or robots meta tag etc. (as is often the case with such redirect scripts) then "no", the links will not be crawled and no rank will be passed. This would make the link essentially a "nofollow" link, similar to when
rel="nofollow" is used directly on the anchor.
Their systems(text editor) only creates links with ...
If this site allows any users to sign up and write arbitrary content then any links should be "nofollow" - in the interests of the site (and everyone really). The links are "untrusted".
Only if the user posting the content has been a member for a while and shown to be trusted might the site allow links posted by that user to be "dofollow". But stress "might".