It's estimated that £2.6m has been issued to South Western Railway (SWR) customers in compensation, since major staff strikes last December.
The train operator says almost 35,000 passengers have claimed because of the disruption, which impacted busy commuter routes to London Waterloo.
SWR is now launching Phase Two of its compensation scheme - encouraging weekly season-ticket holders and daily season-ticket holders to apply.
Around 800 SWR staff who were members of the Rail, Maritime and Transport (RMT) Union opted to walk-out for 27 days, over a long-running dispute about the role of guards.
The union and SWR initially blamed each other, after talks collapsed.
RMT feared the diminishing role of guards on SWR trains could endanger passenger safety.
The union has been demanding that guards should oversee the operation of doors and perform other safety functions when dispatching trains.
However, the train operator called the strikes "unnecessary", claiming it was providing a "much-needed moderninsation" of services.
Did you travel with us during the industrial action in December 2019?— SWR Help (@SW_Help) July 13, 2020
To check your eligibility and make your claim visit https://t.co/CdzfwZVoDc.
An SWR spokesperson said: "During the December 2019 strikes, we carried over 80% of our usual passengers.
"However, given the duration and intensity of the strike, compensation over and above the normal delay repay arrangements is being offered in recognition of the exceptional disruption customers faced".
Claims can be made until 13 September.